Cryptocurrencies and Their Derivatives

Abstract

The objective of this study was to introduce Bitcoin futures and options and Ether futures whose underlying asset is cryptocurrency that different from traditional derivative. And finally focus on cryptocurrency derivative application in hedging price of underlying asset.

To achieve the purpose, first is to introduce cryptocurrency and especially Bitcoin and Ethereum. After explanation of underlying cryptocurrency, the report shows detailed information about Bitcoin and Ether derivative which include the current exist futures and options, definition, trading platform, market mechanics, contract specifications, regulations, fair value price and application. Further, a briefly present the current situation of Bitcoin and altcoin contracts and their derivative contracts in OTC market, which contains ISDA latest launched smart derivative contract introduction.

Key Words: Cryptocurrency, Bitcoin, Bitcoin futures, Bitcoin option, Ethereum, Ether futures, Atomic swap, ISDA, Smart contract

Introduction

Cryptocurrency is a decentralized digital or virtual currency that based on blockchain technology and secured by cryptography. According to CoinMarketCap (2021), there are total 9116 cryptocurrencies with a market cap of 1.98 trillion (as of April 5, 2021). All cryptocurrencies meet the following six conditions: 1. Decentralized, no central authority, distributed achieve consensus on its state. 2. Immutable, the system keeps a sketch of the ownership of cryptocurrency units. 3. The system defines whether new cryptocurrency units can be generated and their origin and ownership. 4.Cryptography can exclusively demonstrate the ownership of cryptocurrency. 5.Even when ownership of cryptographic units is modified, the system allows transections. 6. The system at most perform one of the two instructions that are simultaneous entered for changing ownership of the same cryptographic units(Lansky, 2018).

The cryptocurrency exchange platform is a place allows customers to trade cryptocurrencies for other assets, such as other cryptocurrencies, cash, stocks or precious mental etc. The top five platform in volume are Binance, Coinbase Pro, Huobi Global, Kraken and Bithumb. In the CME group, Bitcoin futures, Options on Bitcoin Futures and Ether Futures are presently listed. Bitcoin Options are listed in Deribit and LedgerX.

Terminology:

Altcoin: All cryptocurrencies that are not Bitcoin

Blockchain: a database or decentralized ledger that stores the ownership of cryptocurrency.

Node: Any computer that connect with the global network Nodes become a node.

Wallet: the software where owner of the cryptocurrencies store. The owner must use a private key to open the wallet and other transactions.

Block: A permanently recorded transection data that appended to the blockchain after it complete.

Hard Fork: Radical change to the protocols of blockchain network result in the validation of previous invalid transection and blocks, or vice versa. Hard forks create a permanent divergence from previous version of blockchain: one path follows the upgraded version, and other continue along the old one. It requires all nodes or users to upgrade to the latest protocol software.

Mining: The process of using computer power to add new blocks to the blockchain (validate transection) with cryptocurrency as reward for successful miner.

ICO: Initial Coin Offering, a financial mechanism for anonymous transferring capital in the form of cryptocurrency to support a project through blockchain.

Token: The return from the project (ICO) in the form of newly generated project-specific currency (Zimmerman, 2020).

Regulation

A critical issue is the regulation and tax of cryptocurrencies which is heterogeneous across countries. In some jurisdictions, Bitcoin is completely banned (e.g., Algeria, Bolivia, Morocco, Nepal, Pakistan, and Vietnam)); in others there is no limit to its use (the U.S., European countries and many others). In addition to restrictions of use, treatment for tax also varies greatly (The Law Library of Congress, 2018). In general, Bitcoin transactions are free from Value-added tax, but gains are subject to tax.  Recently, regulation of cryptocurrencies has been again in the focus of lawmakers, who introduce Bill to clarify regulation of cryptocurrency three times. However, Chair of Federal Reserve Jerome Powell said regulation is not “where it needs to be” when it comes to type of cryptocurrency which has value tied to an outside asset (Smialek, 2021).

Bitcoin

Bitcoin is a cryptocurrency invented in 2008 by an unknown person, group of people or institution using the name Satoshi Nakamoto. Nakamoto posted a white paper called Bitcoin: A Peer-to-Peer Electronic Cash System, which introduced concept of Bitcoin. The Bitcoin market cap was 0.23 Trillion in 2018 and has reached 1.10 Trillion according to CoinMarketCap that compared with 30.436 Trillion of US Dollar market cap in 2018 from Knoema.

The benefit of using Bitcoin, strong protection over money and its transection which is supported by cryptographic signature and proof of work (PoW), and against fraud. Convenient payment and transection without time and space limitation. Moreover, privacy protection, because Bitcoin

is an anonymous payment network and avoid associating with owner’s real-world identity. Nobody except owner themselves know the address of their bitcoin and transection only depend on the new address that every transection happened. Although every transaction is transparent, tractable and recorded permanently, this peer-to-peer transection can happen from one to one, one to some, some to one or some to some from anonymous owners, which dramatically enhance the privacy protection (Bitcoin – Open Source P2P Money, 2021).

The primary concerns towards Bitcoin, Lack of solid anonymity because every transaction is stored in blockchain permanently, which is not traceable currently but may become easy to trace in the future. Wallet can be lost or stolen, and the owner cannot access it anymore. Furthermore, strong volatility of Bitcoin price, which depend directly on the statements of the government, giant enterprise or its representatives. No buyer protection, when goods or other assets are bought through Bitcoin, buyer lack of guarantee from the seller, because the transaction is irreversible (Dumitrescu, 2017).

Table.1, Top 10 competitors of Bitcoin that based on market cap

The field of cryptocurrency has expanded dramatically since last decade, however, Bitcoin continuous lead the cryptocurrency market. The market cap of Bitcoin is almost five times the second one (ETH) and 20 times the third one (BNB), and more than all other cryptocurrencies. It has dominant popularity and more acceptable by public and asset seller and more liquidity. Bitcoin and other cryptocurrencies are their specific technology or function behind, and their primary purpose. For example, Ethereum’s aiming is not establish itself as the alternative to standard currencies (medium of exchange or value storage), but to use its own currency to facilitate programmatic contract (smart contract) and decentralized application platform (marketplace).

Bitcoin History

On October 31, 2008, a anonymous person or group of people (institution) called Satoshi Nakamoto posted Bitcoin P2P e-cash paper that linked to a white paper Bitcoin: A Peer-to-Peer Electronic Cash System. The white paper explains the concept and characteristics of Bitcoin and the technology (algorithm) underlying (Nakamoto, 2018). On January 3, 2009, the first block called genesis block of bitcoin (Bitcoin number 0) was mined with 50 Bitcoin as reward. The first open-source Bitcoin client was launched on January 9, 2009. Programmer Hal Finney is the first receiver of the first Bitcoin transection, and Wei Dai creator of b-money and Nick Szabo creator of bit gold are other early supporters. The amount of Bitcoin is limit that only have one million. The first Bitcoin economic transections were negotiated on the Bitcoin forum about exchanging 10,000 BTC for two pizzas that worth $25. Once Bitcoin became available on exchanges in 2010, it became easier to trade and store (Hicks, 2020). 

Bitcoin price is generally in an uptrend since pizza exchange that worth four Bitcoin per penny. In February 2011, the Bitcoin price crossed the $1 threshold that spend couple of years, which represent few mainstream enthusiasms and traction. After that first bubble occurred, the price surge to $32 and back to $2 at the end of the year. 2013 proved to be a decisive year for Bitcoin price with rising interest from media and internet, especially under the influence from European sovereign debt crisis (Bustillos, 2017). Several bubbles happened after 2013, and in 2017 continuous surge that might related to 2017 Zimbabwean coup d’état place Bitcoin in mainstream spotlight firmly. In March 2020, the COVID-19 early pandemic, the price drops sharply and then recover to a new high on late of the year. 

Today more and more merchants accept Bitcoin for products and services payments like Tesla, more people and institutions are willing to hold Bitcoins. Bitcoin exchange, trading, mining and storage became much more convenient than before, the Bitcoin investment and its derivative as a financial tool have gradually become mature, OTC and regulated exchange both well developed. Regulation and law toward Bitcoin and its related generated by lawmaker. The development of Bitcoin will not cease.

Ethereum is the global, open source and community-run technology powering the cryptocurrency, ether (ETH) and decentralized applications that supported by smart contract. Launched in 2015, in addition to the Bitcoin’s primary function as Pear-to-Pear (P2P) cryptocurrency, the network is a programmable blockchain and anyone who participate can deploy smart contracts and even further advanced and complex structure, such as DApps. Today, it owns the second largest volume in cryptocurrency market.

Ethereum

Ethereum is the global, open source and community-run technology powering the cryptocurrency, ether (ETH) and decentralized applications that supported by smart contract (Ethereum, 2021). Launched in 2015, in addition to the Bitcoin’s primary function as Pear-to-Pear (P2P) cryptocurrency, the network is a programmable blockchain and anyone who participate can deploy smart contracts and even further advanced and complex structure, such as DApps. Today, it owns the second largest volume in cryptocurrency market.

Terminology

Ethereum Virtual Machine: single, canonical computer that everyone on the network agree on , keeps a copy of it and request it to perform computation (transection request). Other participants verify, validate and execute the computation, which cause change in EVM and all transactions are recorded in blockchain once are verified as valid.

Ether: the native cryptocurrency, for the purpose of the existence of a market for computation. The market where participants can verify or execute transection requests and offer computation resources to the network. The transection request need ether as award to who make it works.

Dapps or smart contract: reusable snippet of code (a program, games, marketplaces, financial instruments, etc) that developer provides to EVM memoey and anyone can request and execute it by a transection request.

Literature review

The definition of cryptocurrency is well introduced by Lansky (2018). The Bank of England has a report which shows the technology Blockchain that behind the cryptocurrency (Zimmerman, 2020). The basic cryptocurrencies’ price and volume can be found in CoinMarketCap (2021). The specific introduction, mechanism, advantage and disadvantage of Bitcoin (Bitcoin, 2021) and Ethereum (Ethereum, 2021). The report of regulation of cryptocurrency shows the different laws and regulations towards cryptocurrency in the world (Library of congress, 2018, Regulation of Cryptocurrency). Bitcoin white paper introduce the concept and characteristics of Bitcoin and its underlying technology and algorithms (Nakamoto, 2008). The three-research suggested what influence the Bitcoin price are Kristoufek (2013, 2015), Figà-Talamanca and Patacca (2019) and Kim et al. (2015). Baur (2021) did the research about the volatility of Bitcoin and its role as the medium of exchange and value storage. As for the Bitcoin futures, the paper references the introduction, contract specs, quote, settlement and Rulebook from CME group (CME, 2021, Bitcoin Futures). The pricing of Bitcoin futures and its formular that based on CME group contract specs can be obtained from (Geman, 2019), which also provide the information about plain vanilla option pricing on Bitcoin. Although, CME group announces that Bitcoin futures are regulated, CFTC introduces the detailed regulation method (CFTC, 2017). After launching of Bitcoin futures, there exist influence on Bitcoin returns (Kim, 2019) and price volatility of Bitcoin futures itself (Guo, 2021). Another altcoin futures called Ether futures that offered by CME group has similar characteristics as Bitcoin futures with a few difference (CME, 2021, Ether Futures). Rollover hedging application on Bitcoin with concept support from Ronald (2017)  and Tolbert (2002).The Bitcoin option are different from Bitcoin futures that launched by a standard, well-regulated, matured and world-leading company like CME group, which are launched by some small exchange platform and Fintech start-up company. The option contract from different company is different, Deribit (Deribit, 2021, Options) and LedgerX (LedgerX,2021, Options) offer different contract specification and mechanism. The Bitcoin option pricing is sophisticated and still in research status, however, Stochastic Volatility with a Correlated Jump (SCVJ) model stand high in research estimation and interests and supported by many paper like Hou (2020), Nekhili (2020) and Ivan (2018). The application of Bitcoin option include protective put option strategy with Figlewski(1993) and Dunay (2018) as further reading. For collar options application, real world application from Adkins (2016) is a good example. The smart derivative contract that launched by ISDA with comprehensive detail legal guidance in different specific area (ISDA, 2019, 2020). The introduction and working mechanism are explained by Capco report (Capco, 2019). The example of Bitcoin OTC contract is atomic swap with example explanation (Miraz, 2019).

Bitcoin Futures

First, CME CF Bitcoin Reference Rate (BRR), a regulated daily reference rate of one Bitcoin in U.S. dollar as of 4 p.m. London Time (Bitcoin Overview – CME Group, 2021). Exchanges and trading platforms providing pricing data, including Bitstamp, Coinbase, Gemini, itBit, and Kraken. BRR are calculated based on the relevant transactions of all Constituent Exchanges. Calculation steps on any given calculation day are as follows: All Relevant Transactions are added to a joint list, recording the trade price and size for each transaction. The list is partitioned into a 12 of equally sized five minutes intervals. For each partition separately, the volume-weighted median trade price is calculated from the trade prices and sizes of all relevant transactions. A volume-weighted median differs from a standard median in that a weighting factor, in this case trade size, is factored into the calculation. The BRR is then given by the equally weighted average of the volume-weighted medians of all partitions (Introduction to Bitcoin Reference Rate – CME Group, 2021).

Bitcoin Futures contract (BTC) is a U.S. dollar cash settled and exchange-traded contract that based on BRR, enabling you to speculate on the future price of Bitcoin without holding the underlying cryptocurrency (no Bitcoin wallet or trading platform is needed), which is similar to equity futures. A cash settlement is a settlement method that the seller of the Futures contract does not deliver the Bitcoin but instead transfers the associated cash position on the settlement date. The Chicago Mercantile Exchange (CME) provides monthly cash settlement for Bitcoin futures, which enable futures owner can take cash rather than physical delivery. The Bitcoin Futures in CME group has a value of five times the value of the BRR (U.S. dollar per bit coin), with monthly contract listed for six consecutive months and two additional Dec contract months.   In the upcoming May 3, the CME group will launch Micro Bitcoin Futures, a smaller size (1/10 of one Bitcoin) Bitcoin Futures.

The CBOE Futures Exchange first introduce Bitcoin Futures in December 2017 that followed by CME group. However, since March 2019, CBOE stopped offering new contract. Instead of cash settlement, Bakkt offers physical delivery of Bitcoin. Bitcoin Futures Exchange for Physical (EFP) Transactions I only choose Bitcoin Futures in CME group for following description and

analysis. Bitcoin futures trading of central limit order through the CME Globex platform and clearing by CME ClearPort and CME Direct (Bitcoin Overview – CME Group, 2021).

Bitcoin Futures in CME group is regulated by the Commodity Futures Trading Commission (CFTC), the regulatory body with exclusive jurisdiction over US Bitcoin futures markets. The CME Bitcoin Futures is self-certificated with enhanced standard for oversight over the Bitcoin market and CFTC has limited statutory authority. The CME voluntary chose to give the CFTC the chance to review designated contract markets, derivatives clearing organizations (DCOs), clearing firms and individual traders involved in trading and clearing bitcoin futures. As an extension of this practice, the CFTC will engage in risk-monitoring activities with information sharing, in which it will request voluntary compliance by applicant derivatives exchanges with several criteria, including initial margins requirement, variation margin payment, size and development of the market, positions and changes in positions over time and open interest (CFTC Statement on Self-Certification of Bitcoin Products by CME, CFE and Cantor Exchange | CFTC, 2017).

To enter a Bitcoin Futures, an initial margin deposit and margin maintenance is required The Bitcoin Futures has bid/ask spread, the daily settlement happens between 14:59:00 and 15:00:00 Central Time. The profit or loss is immediately received or paid at the end of every trading day into or from your margin account. When closing the trade, a cash-settlement can close it. Each contract month settles to its volume-weighted average price (VWAP) of all trades that occur between 14:59:00 and 15:00:00 CT. If no trades occur on CME Globex between 14:59:00 and 15:00:00 CT, the settlement period, then the last trade (or the contract’s settlement price from the previous day in the absence of a last trade price) is used to determine whether to settle to the bid or the ask during this period. In the absence of any trade activity or bid/ask in a given contract month during the current trading day, the daily settlement price will be determined by applying the net change from the preceding contract month to the given contract month’s prior daily settlement price. As for the price limit, which is 20% above or below BRR normally, however, due to high volatility of Bitcoin, a special fluctuation limit at 7% above or 13% below.

Although, Bitcoin Futures seems like a FX Futures, they are totally different. FX Futures is a natural and well-developed contract have the option of physical delivery and physical underlying, low margin requirement, low volatility and low contract price that compare with cash-settlement only in Bitcoin Futures with no physical underlying, high margin requirement, high volatility and high contract price.

Moreover, they have different fair value pricing formula.  Normal FX Futures fair value pricing:

F_0=S_0×((1+r_f×days/360))/((1+r×days/360))

where S_0 as spot exchange rate, r as base currency risk free rate and r_f as the foreign currency risk free rate.  As for Bitcoin Future fair value pricing:

F_0=S_0×[1+(r-d)×days/360]

Where S_0 is spot Bitcoin price in U.S. dollar, r as the risk-free rate and d is Bitcoin cost of storage (Geman & Price, 2019). The Bitcoin cannot be viewed as a foreign currency, though, it has exchange rate with U.S. dollar, because risk free rate for Bitcoin is not exist. Therefore, Bitcoin is more like a commodity in fair value pricing. The situation here is the fair value of Bitcoin Futures are less than its quote price, hence, there exist an arbitrage.

The Bitcoin Futures effects on Bitcoin price. The research through the implied volatility of Bitcoin price shows that the Bitcoin market became immediately after the introduction of Bitcoin Futures, but the market gradually become more stable than it was before (Kim et al., 2020). The result is supported by (Shi, 2017) and other research reports. According to Kim et al. (2020), the volatility of Bitcoin Futures price decrease, when the contract approach to maturity.

The key benefits of the Bitcoin Futures: enabling the ability for investor and trader of an underlying cryptocurrency to hedge against future price volatility, and to speculate the market for profit earning. It is a great opportunity for price discovery in a transparent market. Easily trade without entry barrier around wallets and custody (insurance) of the assets. Trustable cash-settlement that based on regulated BRR (Bitcoin Overview – CME Group, 2021). The risk from counterparty almost zero by clearinghouse and regulation, no risk from hack or technical issues toward Bitcoin wallet (no wallet needed), low leverage mitigates the risk of liquidation and margin call when price drop, and limited price decrease the volatile of spot price.

Although Bitcoin Futures is a great mechanism that combine Bitcoin and futures contract, it has some drawbacks as well. The price limit may restrict the potential profit, especially price swing for Bitcoin price is common. The contract size is 5 Bitcoin that has a large contract value, result in a high margin maintenance requirement, which means the contract has high entry level and it is more suitable for institutional trading. The Micro Bitcoin Futures that will be launched might be a greater option for retail trading with relatively lower margin requirement.

Ether Futures

Ether Futures is U.S. dollar cash settle (ETH) and exchange-traded contract that based on ETHUSD_RR, enabling you to speculate on the future price of Bitcoin without holding the underlying Ethereum cryptocurrency (no Ethereum wallet or trading platform is needed). ETH went live on the CME group on February 8, 2021, which after Crypto Facilities (the U.K.) in 2018 and ErisX (the U.S.) in 2020. The following Ether futures only represent the contracts from CME group. Each futures contract is valued at 50 ether, which is defined by CME CF Ether Dollar Reference Rate (ETHUSD_RR) with pricing data from major cryptocurrency exchanges. The ETHUSD_RR, a daily reference rate that was designed by CME group and CF Benchmarks (benchmark administrator), which has same calculation method as BRR. The key benefits of

Ether Futures are easily managed price risk of ether cryptocurrency, transparent and regulated trading and price quotes, and regulated reference rate. The trading and clearing of Ether Futures is regulated by the CFTC with similar situation as Bitcoin Futures. Ether Futures share almost same characteristics as Bitcoin Futures and same fair value pricing method.

Bitcoin/Ether Futures Hedging Application

Bitcoin Futures and Ether Futures share the similar mechanism, the following application are all based on Bitcoin Futures.

Basic Short Hedge

Short hedge is a hedge, a short position in Bitcoin Futures contract, which is appropriate when the investor already own the Bitcoin and expects to sell it in the future date. Using Bitcoin Futures contracts to hedge against the drop of Bitcoin price in the future, due to its unpredictable price move and high volatility. 

The index level l_0 here can also utilize Bitcoin Real Time Index (BRTI) that issued by CME group as the, however, BRTI is a real-time index that published once per second, 24 hours a day, 365 days per year without daily closing price. Therefore, BRR is chosen which announced once a day and have the same calendar as Bitcoin Futures.

Simple hedge ratio:

The hedging problem is the investor owns 100 Bitcoin and want to hedge against the price drop of Bitcoin in two weeks. Since the underlying asset of Bitcoin Futures is the same as the asset being hedged, the hedge ratio: h = 1 that mention in Hull’s. The hedge ratio is the ratio of the position taken in futures contracts to the size of the exposure. The number of futures contracts to hedge the Bitcoin position:

l_0: CME CF Bitcoin Reference Rate (BRR)

m:Bitcoin Futures multiplier (contract size)

P_0:Current value of the Bitcoin fund to hedge

V_F:Current value of one Bitcoin Futures contract

V_F=l_0×m

N=P_0/V_F∶  Number of Bitcoin Futures to hedge the Bitcoin fund

Assume that the Bitcoin BRR movement follow the Bitcoin price volatility index and there are three situations:

σ:Bitcoin price volatility index

Stationary: l_0

Rises:l_0×(1+σ)

Falls:l_0×(1-σ)

Gain/Loss of Bitcoin Futures contract at maturity date:

Gain/Loss∶ 〖(F〗_0 〖-F〗_f)×N×m

Date    4/9/2021

Bitcoin BRR= l_0        58347.48

Interest Rate   5.10%

Dividend Yield 0.00%

Maturity Date  4/21/2021

Days to Maturity         12

Futures Price Quote= F_0      58,760.00

Futures Fair Value      58446.67

Futures multiplier= m  5

Bitcoin Fund to Hedge ($)=〖 P〗_0 5834748.00

Number of futures= N 20

Bitcoin price volatility= σ         3.24%

Table.2, basic information

Simple hedge  BRR Stationary           BRR Rises      BRR Falls

Bitcoin BRR at maturity date= l_f       58347.48         60237.94         56457.02

Bitcoin Fund at maturity date= 〖 P〗_f        5834748.00     6023793.84     5645702.16

Settlement Futures price= F_f            58347.48         60237.94         56457.02

N (unchanged)            20        20        20

Gain/Loss on Bitcoin   0.00     189045.84       -189045.84

Gain/Loss Futures      41252.00         -147793.84      230297.84

Gain/Loss on Bitcoin hedge with futures        41252.00         41252.00         41252.00

Final Portfolio Value   5876000.00     5876000.00     5876000.00

Table.3, basic short hedging with simple hedge ratio performance

Optimal hedge ratio:

When the object of the Bitcoin hedge is minimizing variance, the optimal hedge ratio should be utilized and hedge ratio of 1 is not optimal in this situation. The Bitcoin Futures contracts has the characteristic of daily settlement, therefore, a series of one-day hedge is necessary. Define:

ΔS: one-day percentage changes of BRR, during a period equal the life of the hedge

ΔF: One-day percentage changes of Bitcoin Futures, during a period equal the life of the hedge

σ_S:Standard deviation of ΔS

σ_F:Standard deviation of ΔF

ρ:Correlation between ΔS and ΔF

h:hedge ratio

When the investor is long the Bitcoin and short Bitcoin Futures, the change in the value of the investor’s position during the life of the hedge, ΔV, is:

ΔV=ΔS-hΔF

The variance of ΔV,v,is given by:

v=σ_S^2+〖h^2 σ〗_F^2-2hρσ_S σ_F

Therefore, using first derivative to find minimum of v:

(∂v )/(∂h )=2hσ_F^2-2ρσ_S σ_F

And setting it equal to zero, we find the value of h that minimize the variance is:

h=ρ×σ_S/(σ_F  )

The σ_S and σ_F are historical data that has the same time series as the life of Bitcoin Futures.

Optimal Hedge           

σ_S     0.021

σ_F      0.026

ρ          0.882

h          0.694

Number of futures= N*           14

Table.4, basic information

Optimal Hedge            BRR Stationary           BRR Rises      BRR Falls

Bitcoin BRR at maturity date= l_f       58347.48         60237.94         56457.02

Bitcoin Fund at maturity date= 〖 P〗_f        5834748.00     6023793.84     5645702.16

Settlement Futures price= F_f            58347.48         60237.94         56457.02

N* (unchanged)           13        13        13

Gain/Loss on Bitcoin   0.00     189045.84       -189045.84

Gain/Loss Futures      26813.80         -96065.99        149693.59

Gain/Loss on Bitcoin hedge with futures        26813.80         92979.84         -39352.24

Final Portfolio Value   5861561.80     5927727.84     5795395.76

Table.5, basic short hedging with optimal hedge ratio performance

Calendar Spreads Hedging

Calendar spread strategy, the hedger can simultaneous entering a long and short position on the Bitcoin Futures, however, with different maturity month to be filled at specific price difference between the contracts. The strategy is the outcome of finite lifetime of futures contract and a property that periodically forces both near term and long-term investor to exchange their contracts with different maturity date.

The hedging problem is the investor want to buy 100 Bitcoin in seven months later, because of currency shortage to cover 100 Bitcoin now (August 1,2020) and afraid of Bitcoin surge in the future (April). The strategy is maintaining a long Bitcoin Futures on Bitcoin over six months. Although Bitcoin Futures in CME group has listed six consecutive months and two additional Dec months (if Dec in consecutive months, then only one additional Dec), it only list until March (Oct, Nov, Dec, Dec (additional), Jan, Feb, March). Moreover, there exist risk of liquidity for the contracts beyond six months. In such case, a roll-over hedge is necessary, which is a type of calendar spread. Firstly, long a one-month Bitcoin Futures, and then close the futures contract near the maturity and long another Bitcoin Futures that expire in one month later to roll the position over just prior to each delivery month. One-month futures contract for hedging is the most liquid choice.

Time t_0  (Oct)∶Long Bitcoin Futures Contract 1

Time t_1  (Oct):Close out Contract 1,long Bitcoin Futures Contract 2

Time t_2  (Nov):Close out Contract 2,long Bitcoin Futures Contract 3

Time t_3  (Dec):Close out Contract 3,long Bitcoin Futures Contract 4

Time t_4  (Jan):Close out Contract 4,long Bitcoin Futures Contract 5

Time t_5  (Feb):Close out Contract 5,long Bitcoin Futures Contract 6

Time t_6  (Mar):Close out Contract 6,long Bitcoin Futures Contract 7

Time t_7  (Apr):Close out Contract 7

The number of hedging futures contracts, N,  is calculated through simple hedge ration method.

〖The Bitcoin fund net cost= C〗_f+Gain or Loss in futures contracts

〖 GLF〗_i 〖=(F〗_(0,i-1)-〖 F〗_(f,i-1))×m×N,for i=1,2,3,4,5,6,7

Gain or Loss in all futures contracts=∑_(i=1)^7▒〖〖 GLF〗_i  〗

Futures Price  Initial=〖 F〗_0,0       Close=〖 F〗_(f,i-1)   Open=〖 F〗_(0,i)      Gain/Loss in futures=〖 GLF〗_i

Oct, i=1           10645  13479  13845  283400

Nov, i=2                       13735  16628  -11000

Dec, i=3                       19730  23685  310200

Jan, i=4                       37242  34855  1355700

Feb, i=5                       47002  46325  1214700

March, i=6                   53346  54060  702100

April, i=7                      58760              470000

Table.6, calendar spread hedging monthly information

Buy Bitcoin Date= t_7 4/9/2021

BRR= l_0        10623.33

Bitcoin Fund Cost at t_0=〖 C〗_0   -1062333

m         5

N         20

Initial futures cost        -212900

Bitcoin BRR at t_7= l_f           58347.48

Bitcoin fund cost t_7= C_f      -5834748

Gain/Loss in all futures           4325100

Bitcoin fund net cost   -1722548

Table.7, calendar spread hedging with simple hedge ratio performance

The Bitcoin price increase from $10623.33 to $58347.48, and hedger receives $4325100 compensation for price surge. Although the cost of buying Bitcoin has 4.5 times the original one, only 1.6 times after hedging.

Bitcoin Options

The Bitcoin Option Trading in the U.S. is legal since CFTC approved and issued LedgerX for Derivatives Clearing Organization (DCO) on October 2, 2017. LedgerX is a digital currency options and futures exchange and clearinghouse that regulated by CFTC. The Bitcoin Mini Option offered by LedgerX is a European style that the option exercise only at expiration.  The contract size is 0.01 Bitcoin, and trading hours is 24 hours per day and seven days per week (Options, 2021). The settlement in LedgerX is physical-settled and there is no auto-exercise, where investor should submit exercise instrument on the platform. More detail, trader determined whether that option is in the money, at the money or out of the money, which means they can factor in different exchanges and different benchmarks for underlying Bitcoin price. Therefore, platform do the delivery of the trade and cannot manipulate for profit through determine whether Bitcoin price hit the strike price and give trader more flexibility and determination. When investors exercise long call options, they should have enough US dollar that deposited on the platform to buy Bitcoin at the U.S. dollar strike price. As for long put options, investors are required to have enough Bitcoin on the platform to sell Bitcoin at the U.S. dollar strike price. Closing out of a position is available any time before expiration, which means investors can close a short position by purchasing the number of option contracts that they are short or close a long position by selling the number of option contracts that they are long. When execute close out of short position, the position will be zero and position locked collateral for previous short position will be closed. And when execute close out of long position, no short collateral is required. The Chief Operation Officer of LedgerX said that people like miner who owe Bitcoin are exposure to the risk of U.S. dollar versus Bitcoin can hedge directly through pledging it directly or selling it, rather than convert it to dollar then use dollar to hedge (Shin, 2019). The option is a great and helpful tool for who in their consumer-facing or merchant-facing business that have bitcoin on their balance sheet to hedge their risk on their balance sheet, which are similar to large oil producers or refinery do. Another characteristic is Bitcoin Option is negotiated trades that people propose a price and size and show the trade on the exchange, all of fully collateralized options are centrally cleared by the LedgerX clearinghouse. Therefore, there exist bid/offer for exchange.

There exists lots of difference between Bitcoin Options and other FX options. The price of Bitcoin Options contact is far more expansive than FX option contact price. The reason is Bitcoin has higher implied volatility than FX rate which means a higher price or more expensive the premium is likely to be.

Unregulated Bitcoin Option exchange that provided by Derbit. After LedgerX, OKEx launched options trading on December 27, 2019.

Deribit has dominant Bitcoin Option market share since 2016 when the company come to exist, and it has different characteristic as Bitcoin Option in LedgerX. In Deribit, the Bitcoin Option is cash-settlement that the options writer will pay any profit due to the holder rather than transferring asset. The underlying is Deribit BTC Index, however, when there exist a corresponding future has same day as expiration that futures price will be used. The order size that greater than 0.1 option contract is allowed. The order can be filled, and price can be determined through BTC or additional advanced order type (U.S. dollar and implied volatility) at trader’s preference. The price of the option in order book is priced at BTC, which means the option price equal how many Bitcoin. If options expired in the money, the exercise is automatic with cash settlement in the equivalent of Bitcoin.

Bitcoin Option Pricing

The pricing model used here is Black-Scholes model. There exists more advanced pricing model Stochastic Volatility with a Correlated Jump (SVCJ) model with numerous paper and research prove its suitable for Bitcoin option pricing, because option prices are strongly driven by jumps in the returns and volatility process of Bitcoin (Chen et al., 2018). Moreover, Kou Jump-Diffusion model shows the goodness of fit, but there is no significant difference with Black-Scholes model (Silva, 2018). Bitcoin price itself does not follow the lognormal pattern with excess kurtosis. Although Black-Scholes model is not the perfect choice for Bitcoin option pricing, we still use here as a benchmark pricing model for at the money option. Furthermore, the characteristic of Bitcoin option has broken some limits: no dividend payout and no early exercise.

Assume Bitcoin price has the lognormal distribution and follow the random walk property (geometric Brownian motion with constant drift and volatility), there exist no transection cost and no arbitrage opportunity, ability to borrow and lend any amount at risk free rate and buy and sell any amount of Bitcoin and having risk free rate.

Black-Scholes model pricing formular:

Call option=S_t N(d_1 )-Ke^(-r(T-t) ) N(d_2 )

Put option=Ke^(-r(T-t) ) N(〖-d〗_2 )-S_t N(〖-d〗_1 )

d_1=(ln⁡(S_t/K)+(r+σ^2/2)(T-t))/(σ√(T-t)),d_2=d_1-σ√(T-t)

Where N(x) function is the cumulative probability distribution function for a variable with standard normal distribution. K is the strike price of options, r is the risk-free rate that quotedfrom U.S Treasury daily yield curve rate, T is maturity date and t is the options trading

date, S_t is the Bitcoin price at trading date and σ is the volatility of Bitcoin price. The volatility here can be quoted from Bitcoin volatility index that depend on the exchange platform where offer the option trading.

Every exchange platform that provides Bitcoin option trading service have its own pricing model that supported by risk management team, therefore, the quoted price and implied volatility that obtained from Black-Scholes model are different. Another pricing method Binomial tree risk neutral model, when using sufficient number of steps, the price obtained from Binomial tree is identical to the Black-Scholes model.

Bitcoin Options hedging application

Protective Put Option

Traditionally, when investor hold underlying asset, long a put option is useful to hedge against the price decrease of underlying asset that is based on investor bearish on the asset. However, when Bitcoin as the underlying asset, the price of Bitcoin in the long term is bullish. Due to Bitcoin high volatility and sometimes plummet in a short time, a protective put hedging strategy is attractive when it comes to Bitcoin hedging. The potential goals why an investor might choose the strategy are limiting risk when holding Bitcoin and guard against previously purchased Bitcoin to hedge against short term uncertainty and potential loss, without sacrificing a majority of potential increase. The strategy is hold a position in Bitcoin and long put options with strike price that similar the current price of Bitcoin.

The hedging problem is the investor hold 100 Bitcoin and what to hedge against unexpected price fall in the following week, but still bullish the Bitcoin price trend in the future.

The payoff and P/L from protective put that based on initial Bitcoin price, Bitcoin put option premium paid, strike price and underlying price at maturity date.

Payoff at maturity=max(K-I_T,0)×N+(I_T-I_0 )×n-P×N

Breakeven price=I_0+P×N

N=  (I_0×n)/(I_0×m):Number of Bitcoin put option for hedging

Protective Put Portfolio          

Trade date       4/15/2021

Strike price= K 62000

Maturity date   4/23/2021

Bitcoin put option premium= P           1340.50

Underlying Bitcoin Price at trading date= I_0             63831.05

Implied volatility= IV    59.40%

Risk free rate  1.64%

Multiplier= m   1

Number of Bitcoin= n  100

Number of put option= N        100

Number of put option (delta hedging) = N_Δ 263

Delta of Bitcoin=Δ_b   1

Delta of put option= Δ_p         -0.349

Table.8, protective put hedging strategy basic information

Simulate 11001 situations that Bitcoin price on April 4, 2021 that range from $55000 to $66000.

Fig.1, protective put payoff vs Bitcoin position payoff

The maximum profit for Protective put strategy is infinite, which is only reduced by the fixed amount of put options premium paid (relatively expansive that compare to other underlying assets options). The maximum loss is limited, once future Bitcoin price below the strike price will be compensated by the put option profit.

As for the delta neutral hedging in protective put, which enable the Bitcoin position to continue to profit if the Bitcoin price rises or falls strongly. Especially when price fall dramatically, the portfolio can gain infinite profit that compare with limited and fixed loss if normal hedging. Although the maximum profit is infinite, the premium cost increase that due to the more contracts required to delta neutral hedging than normal hedging which limits the profit. Therefore, there exists lower and upper breakeven price, when price above upper price and lower

than down price, the portfolio can make profit. Because delta neutral hedging consist of neutralize the move in option price and Bitcoin price, which requires rebalancing number of option contracts constantly to avoid being over or under hedged. When using Black-Scholes pricing model as a benchmark, the Δ_p=-N(-d_1 )=N(d_1 )-1.

N_Δ=(n×Δ_b)/(-Δ_p ):Number of Bitcoin put option for delta hedgin

Maximum loss=(K-I_0 )×n-P×N_Δ

Upper breakeven price=(P×N_Δ-I_0×n)/n

Down breakeven price=  (〖K×N〗_Δ-P×N_Δ-I_0×n)/(I_0 〖×(N〗_Δ-n))

Fig.2, protective put payoff vs Bitcoin position payoff with delta neutral hedging

To obtain a better understand of protective put strategy work in different trending environment, simulated and analyses the path of bitcoin through geometric random walks. 1000 simulations were used for three different scenarios with portfolio and Bitcoin returns were calculated as output. Using the past 111 days of Bitcoin historical natural log-return and then calculating the drift of value 0.0116 that based on the average of log-returns with volatility incorporated. With positive drift, the trend of simulated price goes up and unhedged Bitcoin position has a better average return which makes the hedge less necessary. For the negative drift, -0.0116 was used

that is the negative counterpart of the value in positive drift random walk. The drift implied a downward trend of Bitcoin price and a better average return in hedged portfolio.

μ_log:Average of historical log-returns

σ:Standard deviation of historical log-returns

μ=μ_log+σ^2/2:drift

I_(t+1)=I_t×e^((μ-0.5×σ^2 )×1)+σ×√1×z,with z as normal distribution

Portfolio return:(Max(0,K-I_T )-P+I_T-I_0)/(I_0+P)

drift      0.0116 0.0000 -0.0116

σ          4.67%  4.67%  4.67%

4/15/2021=I_0 63831.05         63831.05         63831.05

4/16/2021=I_1 64506.55         63761.65         63025.29

4/17/2021=I_2 65189.09         64436.26         62229.75

4/18/2021=I_3 65878.79         65118.2           61444.18

4/19/2021=I_4 66575.93         65807.07         60668.47

4/20/2021=I_5 67280.46         66503.44         59902.54

4/21/2021=I_6 67992.36         67207.13         59146.35

4/22/2021=I_7 68711.81         67918.31         58399.71

4/23/2021=I_8 69438.86         68636.98         57662.48

I_T       69439.11         68637.21         57662.25

Average portfolio return          6.55%  5.32%  -4.87%

Bitcoin return   8.79%  7.53%  -9.66%

Table.9, simulations and protective put hedging performance

Collar hedging strategy:

Collar option hedging strategy is employed to decrease both negative and positive return of Bitcoin, which hedge against potential volatility of Bitcoin price. The collar position is composed of holding the Bitcoin position, longing out of the money put option contracts and shorting out of the money call option contracts. More conveniently, a combination of using protective put option and covered call option.

Collar  

Today  4/23/2021

Bitcoin price underlying=〖 I〗_0      50042.59

Number of Bitcoin= n  100

Bitcoin position            5004259

Put option premium=P_P       1376.19

Put option maturity date          4/30/2021

Put option strike price= K_P   48000

Put option implied volatility=〖IV〗_P           0.888

Number of put option contracts= N_P            100

Call option premium=〖 P〗_C         1326.14

Call option implied volatility= 〖IV〗_C         0.793

Call option maturity date         4/30/2021

Call option strike price= K_C  52000

Number of call option contracts= N_C           100

Table.10, collar option hedging strategy basic information

Fig.3, collar option payoff vs Bitcoin position payoffs vs protective put option payoff

By taking a long position in OTM put option and short position in OTM call option, when price drop below the put option strike price, the compensation from options aggregate, when price rise above the call option strike price, the loss from options aggregate. If the value of Bitcoin price between two strike prices, the loss experienced by put option offset by gain from call option. In the chart below, the price below the K_P  and above K_C the payoff is flat with limit potential downside and upsize, and between the strike price the payoff almost same as payoff of Bitcoin position.  The strategy allows covered call option sold to cover the cost from protective put option, and still allows potential upward of Bitcoin price and protect against large loss. On April 23, 2021, Bitcoin price has experienced a dramatically drop, which has high down-size risk with low probability uptrend in the short-term but a strong long-term potential. In this situation, an almost free cost hedging strategy is more attractive to hedger. When it compared with protective put, the hedger can benefit from collar strategy that has lower cost, more price downward compensation and lower breakeven price.

The investor holds 100 Bitcoin and decided to hedge through Collar hedging strategy, who has experienced one-week continuous price decline and afraid of further huge price drop. The number of put option contracts and call option contracts are same and calculated by the same method as protective put. Simulation of future Bitcoin price shares the same method as protective put option. Using past two weeks average log-return with standard deviation incorporated as drift that represent current Bitcoin price trend. It is obvious that simulated Bitcoin price in downward trend with drift value of -0.0093.

Portfolio payoff=n(I_T-I_0 )+[Max(K_P-I_T,0)-P_P]N_P+〖[P〗_C-Max(I_T-K_C,0)]N_C

Breakeven price= 〖 I〗_0+P_C-P_P

Maximum gain=K_C-P_P-〖 I〗_0

Maximum loss=K_P+P_C-〖 I〗_0

drift      -0.0093            0.0000 0.0093

σ          0.03216           0.03216           0.03216

4/23/2021=I_0 50042.59         50042.59         50042.59

4/24/2021=I_1 49555.41         50016.67         50482.22

4/25/2021=I_2 49073.04         49990.8           50925.75

4/26/2021=I_3 48595.31         49964.95         51373.12

4/27/2021=I_4 48122.28         49939.14         51824.47

4/28/2021=I_5 47653.82         49913.29         52279.78

4/29/2021=I_6 47189.95         49887.55         52739.13

4/30/2021=I_7 46730.62         49861.82         53202.49

=I_T     46730.75         49861.76         53202.57

Average portfolio return          -4.18% -0.46% 3.81%

Bitcoin return   -6.62% -0.36% 6.31%

Table.11, simulations and collar option hedging strategy performance

OTC Bitcoin market

The Over the Counter (OTC) Bitcoin market acts as an alternative to exchanges, which is another less formal method to trade Bitcoin and its derivatives (also NFT). OTC has no exchange as market maker between buyers and sellers and connects them directly. There is no physical location, buyers and sellers should communicate through forums, chatrooms, telegram, LinkedIn, or OTC broker, etc. People who want to trade Bitcoin or its derivatives will quote the prices they wish to sell or buy. According to Bloomberg reported that the daily cryptocurrency OTC has $15 billion market size that compared with $250 million to$30 billion per day in total OTC market size (Kharif, 2018). Today, the generally daily OTC volume for cryptocurrency is much larger than exchanged volume, for example Circle said OTC market is three times the regular exchanged and Aite group’s research showed that 65% of trading volume happen in the OTC market. The first OTC Bitcoin market is Circle, which was launched because miner need a place to sell large amount of mined Bitcoin immediately. The miner as the main seller in OTC market and hedge fund as main buyer, and sometimes regulated broker-dealer or exchange OTC desks involved (Editorial Team, 2019).

There are some advantages why people or institutions prefer OTC marker for trading. Increasing liquidity: cryptocurrency exchanges have low liquidity; however, OTC market provide opportunity for large trading orders of cryptocurrency quickly. Price protection: trading in OTC market even in large amount does not impact the cryptocurrency’s price (except news dissemination about large amount trading), and no slippage (executed price distinct from expected price). Anonymity: different from trading in exchange platform that easy to track, order in OTC desk does not show up. No amount limitation: the majority exchange platform limit trading and withdraw per day. More token varieties choice: there are limit choice of cryptocurrency, derivatives, tokens, NFT or smart contracts for trading.

The disadvantages are obvious. Settlement risk or counterparty risk: limit deliver, or cash payment guaranteed (especially when large order happened) and not all OTC brokers offer custody solutions. Missing regulation: even though some OTC brokers and desk are regulated, when compare with exchanged-trading platform is not enough and most of OTC market is unregulated. Today, emerging software such as Caspian, OTCXC and Fidelity are launched to protect institutional or single users to securely trading in OTC market.

Swap

Atomic swap: crypto-to crypto swap, exchanging one type of cryptocurrency to another (exchange Bitcoin to Litecoin). A peer-to-peer trades across different blockchain of different cryptocurrency, which allows people to exchange their coins directly from their wallet without

third party participated that based on smart contracts. The key technology and algorithm is Hash Timelock Contracts (HTLC). Hashlock and Timelock form the HTLC, which create a trust rule between two counterparties that prevent executing partially. A example can easily explain how Hashlock works. Institution A deposit Bitcoins into a contract address that works like a 〖safe〗_A, and at same time generate a key to the 〖safe〗_A. Then A share the cryptographic hash of key to the institution B, but B cannot open the safe now. B uses the hash that offered by A to create a 〖safe〗_(B )to store Litecoins. To claim Litecoins, A can use the real key to open the 〖safe〗_B that has the same hash as 〖safe〗_A, meanwhile, A reaveals the real key to B and B can get access to 〖safe〗_A at the same time. The Hashlock is what prevent either parties to access counterparties’ fund without key or data revealed (〖safe〗_A’s key).

The main advantage of atomic swap are utilizing decentralized characteristic that cryptocurrency have that two parties do not need to offer their wallet or funds to exchange or third party. The trading happens quickly and has almost zero trading fees and operational cost. Furthermore, altcoins can also exchange with each other without using Bitcoin as an intermediary cryptocurrency.

Smart derivative contract

There are numerous possible definitions for smart derivative contract and one of the best definitions according to Legal Guidelines for Smart Derivatives Contracts: Introduction published by ISDA in 2019 is: a smart contract is a contract which include automatically performed computer code in pre-defined condition and some may require human input and control. It is an efficient derivative that incorporated with computer code which are automatically and irreversible. When it comes to risk management purpose, the industry participants will retain human involvement (Legal Guidelines for Smart Derivatives Contracts: Introduction – International Swaps and Derivatives Association, 2019). The potential benefits the smart contract provide to people are better regulation, reduced complexity and cost, and increased efficiency. The market participant following the same frame and automatically working, which decrease the time cost that required to negotiate contracts.

The smart derivative contracts are being used in the near term. ISDA published a series of Legal Guidelines for Smart Derivatives Contracts: Foreign Exchange Derivatives, Credit Derivative, and Interest Rate Derivatives. The purpose of these guidelines is to support smart derivatives contracts developers and other main stakeholder through explaining the core principles of ISDA documentation and raising awareness of the important legal and regulatory issues they should consider when developing and deploying such solutions within the derivatives market.

Moreover, the guideline identifies the potential application of such technology to the specific market. ISDA first proposed a standardized solution (or common language) Common Derivatives Model (CDM) in 2017, providing market participant a lifecycle common digital representation in derivative trading. Barclays is the first institution making blockchain application in reality through CDM. The Distributed ledger technology (DLT) is one of the key parts of smart derivatives contracts. In essence, DTL provide data and record that available for all participants with only one centralized record of data. Only unanimous agreement among all parties can change record in DTL. In smart derivative contract, DTL can restrict access to only participant and regulators. The DTL contribute to bind participants and help them dealt complexity among automatically derivative trading and data collection (What Is the ISDA CDM? – International Swaps and Derivatives Association, 2018).

Summary and Further Suggestions:

From this report, we realized the popularity and growing attention toward cryptocurrency especially Bitcoin and Ethereum. The high volume of cryptocurrency trading and exchange promote the flourish and gradually mature of Bitcoin derivative and Ethereum derivative in exchange-trading and OTC markets. The standard platform, contract and regulation and law involved has become normal situation in cryptocurrency market. Moreover, Rollover futures hedging, protective put and collar option hedging that frequently utilized in traditional derivative hedging area are proved workable and helpful in hedging cryptocurrency. The cryptocurrency futures fair value pricing and Black-Scholes model in option pricing could be viewed as a benchmark price. The successful application of cryptocurrency derivative will arouse investors and hedgers’ attention and interests, which will increase investment, research and development in derivatives. OTC market since it appeared, Bitcoin derivative contracts and other altcoin derivative contracts are well-developed. With the launch of smart derivative contract, the ISDA offers participants a standard language for future cryptocurrency OTC derivative development.

Studying and research of cryptocurrency derivative has a long way to go, especially since cryptocurrency owns different characteristics that compare with traditional commodity, foreign currency or equity as underlying asset. When it comes to derivative pricing, there not exit a popular and generally accept pricing methods like Black-Scholes model, and pricing model that designed for traditional asset may not be suitable for cryptocurrency derivatives, new and advanced pricing model and valuation method required more researchers’ attention and effort. And the launch and development of derivative may have impact on price, return and volatility of underlying asset, a few reports talked about the question and need more research to prove it.

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Cryptocurrencies and Their Derivatives

Abstract

The objective of this study was to introduce Bitcoin futures and options and Ether futures whose underlying asset is cryptocurrency that different from traditional derivative. And finally focus on cryptocurrency derivative application in hedging price of underlying asset.

To achieve the purpose, first is to introduce cryptocurrency and especially Bitcoin and Ethereum. After explanation of underlying cryptocurrency, the report shows detailed information about Bitcoin and Ether derivative which include the current exist futures and options, definition, trading platform, market mechanics, contract specifications, regulations, fair value price and application. Further, a briefly present the current situation of Bitcoin and altcoin contracts and their derivative contracts in OTC market, which contains ISDA latest launched smart derivative contract introduction.

Key Words: Cryptocurrency, Bitcoin, Bitcoin futures, Bitcoin option, Ethereum, Ether futures, Atomic swap, ISDA, Smart contract

Introduction

Cryptocurrency is a decentralized digital or virtual currency that based on blockchain technology and secured by cryptography. According to CoinMarketCap (2021), there are total 9116 cryptocurrencies with a market cap of 1.98 trillion (as of April 5, 2021). All cryptocurrencies meet the following six conditions: 1. Decentralized, no central authority, distributed achieve consensus on its state. 2. Immutable, the system keeps a sketch of the ownership of cryptocurrency units. 3. The system defines whether new cryptocurrency units can be generated and their origin and ownership. 4.Cryptography can exclusively demonstrate the ownership of cryptocurrency. 5.Even when ownership of cryptographic units is modified, the system allows transections. 6. The system at most perform one of the two instructions that are simultaneous entered for changing ownership of the same cryptographic units(Lansky, 2018).

The cryptocurrency exchange platform is a place allows customers to trade cryptocurrencies for other assets, such as other cryptocurrencies, cash, stocks or precious mental etc. The top five platform in volume are Binance, Coinbase Pro, Huobi Global, Kraken and Bithumb. In the CME group, Bitcoin futures, Options on Bitcoin Futures and Ether Futures are presently listed. Bitcoin Options are listed in Deribit and LedgerX.

Terminology:

Altcoin: All cryptocurrencies that are not Bitcoin

Blockchain: a database or decentralized ledger that stores the ownership of cryptocurrency.

Node: Any computer that connect with the global network Nodes become a node.

Wallet: the software where owner of the cryptocurrencies store. The owner must use a private key to open the wallet and other transactions.

Block: A permanently recorded transection data that appended to the blockchain after it complete.

Hard Fork: Radical change to the protocols of blockchain network result in the validation of previous invalid transection and blocks, or vice versa. Hard forks create a permanent divergence from previous version of blockchain: one path follows the upgraded version, and other continue along the old one. It requires all nodes or users to upgrade to the latest protocol software.

Mining: The process of using computer power to add new blocks to the blockchain (validate transection) with cryptocurrency as reward for successful miner.

ICO: Initial Coin Offering, a financial mechanism for anonymous transferring capital in the form of cryptocurrency to support a project through blockchain.

Token: The return from the project (ICO) in the form of newly generated project-specific currency (Zimmerman, 2020).

Regulation

A critical issue is the regulation and tax of cryptocurrencies which is heterogeneous across countries. In some jurisdictions, Bitcoin is completely banned (e.g., Algeria, Bolivia, Morocco, Nepal, Pakistan, and Vietnam)); in others there is no limit to its use (the U.S., European countries and many others). In addition to restrictions of use, treatment for tax also varies greatly (The Law Library of Congress, 2018). In general, Bitcoin transactions are free from Value-added tax, but gains are subject to tax.  Recently, regulation of cryptocurrencies has been again in the focus of lawmakers, who introduce Bill to clarify regulation of cryptocurrency three times. However, Chair of Federal Reserve Jerome Powell said regulation is not “where it needs to be” when it comes to type of cryptocurrency which has value tied to an outside asset (Smialek, 2021).

Bitcoin

Bitcoin is a cryptocurrency invented in 2008 by an unknown person, group of people or institution using the name Satoshi Nakamoto. Nakamoto posted a white paper called Bitcoin: A Peer-to-Peer Electronic Cash System, which introduced concept of Bitcoin. The Bitcoin market cap was 0.23 Trillion in 2018 and has reached 1.10 Trillion according to CoinMarketCap that compared with 30.436 Trillion of US Dollar market cap in 2018 from Knoema.

The benefit of using Bitcoin, strong protection over money and its transection which is supported by cryptographic signature and proof of work (PoW), and against fraud. Convenient payment and transection without time and space limitation. Moreover, privacy protection, because Bitcoin

is an anonymous payment network and avoid associating with owner’s real-world identity. Nobody except owner themselves know the address of their bitcoin and transection only depend on the new address that every transection happened. Although every transaction is transparent, tractable and recorded permanently, this peer-to-peer transection can happen from one to one, one to some, some to one or some to some from anonymous owners, which dramatically enhance the privacy protection (Bitcoin – Open Source P2P Money, 2021).

The primary concerns towards Bitcoin, Lack of solid anonymity because every transaction is stored in blockchain permanently, which is not traceable currently but may become easy to trace in the future. Wallet can be lost or stolen, and the owner cannot access it anymore. Furthermore, strong volatility of Bitcoin price, which depend directly on the statements of the government, giant enterprise or its representatives. No buyer protection, when goods or other assets are bought through Bitcoin, buyer lack of guarantee from the seller, because the transaction is irreversible (Dumitrescu, 2017).

Table.1, Top 10 competitors of Bitcoin that based on market cap

The field of cryptocurrency has expanded dramatically since last decade, however, Bitcoin continuous lead the cryptocurrency market. The market cap of Bitcoin is almost five times the second one (ETH) and 20 times the third one (BNB), and more than all other cryptocurrencies. It has dominant popularity and more acceptable by public and asset seller and more liquidity. Bitcoin and other cryptocurrencies are their specific technology or function behind, and their primary purpose. For example, Ethereum’s aiming is not establish itself as the alternative to standard currencies (medium of exchange or value storage), but to use its own currency to facilitate programmatic contract (smart contract) and decentralized application platform (marketplace).

Bitcoin History

On October 31, 2008, a anonymous person or group of people (institution) called Satoshi Nakamoto posted Bitcoin P2P e-cash paper that linked to a white paper Bitcoin: A Peer-to-Peer Electronic Cash System. The white paper explains the concept and characteristics of Bitcoin and the technology (algorithm) underlying (Nakamoto, 2018). On January 3, 2009, the first block called genesis block of bitcoin (Bitcoin number 0) was mined with 50 Bitcoin as reward. The first open-source Bitcoin client was launched on January 9, 2009. Programmer Hal Finney is the first receiver of the first Bitcoin transection, and Wei Dai creator of b-money and Nick Szabo creator of bit gold are other early supporters. The amount of Bitcoin is limit that only have one million. The first Bitcoin economic transections were negotiated on the Bitcoin forum about exchanging 10,000 BTC for two pizzas that worth $25. Once Bitcoin became available on exchanges in 2010, it became easier to trade and store (Hicks, 2020). 

Bitcoin price is generally in an uptrend since pizza exchange that worth four Bitcoin per penny. In February 2011, the Bitcoin price crossed the $1 threshold that spend couple of years, which represent few mainstream enthusiasms and traction. After that first bubble occurred, the price surge to $32 and back to $2 at the end of the year. 2013 proved to be a decisive year for Bitcoin price with rising interest from media and internet, especially under the influence from European sovereign debt crisis (Bustillos, 2017). Several bubbles happened after 2013, and in 2017 continuous surge that might related to 2017 Zimbabwean coup d’état place Bitcoin in mainstream spotlight firmly. In March 2020, the COVID-19 early pandemic, the price drops sharply and then recover to a new high on late of the year. 

Today more and more merchants accept Bitcoin for products and services payments like Tesla, more people and institutions are willing to hold Bitcoins. Bitcoin exchange, trading, mining and storage became much more convenient than before, the Bitcoin investment and its derivative as a financial tool have gradually become mature, OTC and regulated exchange both well developed. Regulation and law toward Bitcoin and its related generated by lawmaker. The development of Bitcoin will not cease.

Ethereum is the global, open source and community-run technology powering the cryptocurrency, ether (ETH) and decentralized applications that supported by smart contract. Launched in 2015, in addition to the Bitcoin’s primary function as Pear-to-Pear (P2P) cryptocurrency, the network is a programmable blockchain and anyone who participate can deploy smart contracts and even further advanced and complex structure, such as DApps. Today, it owns the second largest volume in cryptocurrency market.

Ethereum

Ethereum is the global, open source and community-run technology powering the cryptocurrency, ether (ETH) and decentralized applications that supported by smart contract (Ethereum, 2021). Launched in 2015, in addition to the Bitcoin’s primary function as Pear-to-Pear (P2P) cryptocurrency, the network is a programmable blockchain and anyone who participate can deploy smart contracts and even further advanced and complex structure, such as DApps. Today, it owns the second largest volume in cryptocurrency market.

Terminology

Ethereum Virtual Machine: single, canonical computer that everyone on the network agree on , keeps a copy of it and request it to perform computation (transection request). Other participants verify, validate and execute the computation, which cause change in EVM and all transactions are recorded in blockchain once are verified as valid.

Ether: the native cryptocurrency, for the purpose of the existence of a market for computation. The market where participants can verify or execute transection requests and offer computation resources to the network. The transection request need ether as award to who make it works.

Dapps or smart contract: reusable snippet of code (a program, games, marketplaces, financial instruments, etc) that developer provides to EVM memoey and anyone can request and execute it by a transection request.

Literature review

The definition of cryptocurrency is well introduced by Lansky (2018). The Bank of England has a report which shows the technology Blockchain that behind the cryptocurrency (Zimmerman, 2020). The basic cryptocurrencies’ price and volume can be found in CoinMarketCap (2021). The specific introduction, mechanism, advantage and disadvantage of Bitcoin (Bitcoin, 2021) and Ethereum (Ethereum, 2021). The report of regulation of cryptocurrency shows the different laws and regulations towards cryptocurrency in the world (Library of congress, 2018, Regulation of Cryptocurrency). Bitcoin white paper introduce the concept and characteristics of Bitcoin and its underlying technology and algorithms (Nakamoto, 2008). The three-research suggested what influence the Bitcoin price are Kristoufek (2013, 2015), Figà-Talamanca and Patacca (2019) and Kim et al. (2015). Baur (2021) did the research about the volatility of Bitcoin and its role as the medium of exchange and value storage. As for the Bitcoin futures, the paper references the introduction, contract specs, quote, settlement and Rulebook from CME group (CME, 2021, Bitcoin Futures). The pricing of Bitcoin futures and its formular that based on CME group contract specs can be obtained from (Geman, 2019), which also provide the information about plain vanilla option pricing on Bitcoin. Although, CME group announces that Bitcoin futures are regulated, CFTC introduces the detailed regulation method (CFTC, 2017). After launching of Bitcoin futures, there exist influence on Bitcoin returns (Kim, 2019) and price volatility of Bitcoin futures itself (Guo, 2021). Another altcoin futures called Ether futures that offered by CME group has similar characteristics as Bitcoin futures with a few difference (CME, 2021, Ether Futures). Rollover hedging application on Bitcoin with concept support from Ronald (2017)  and Tolbert (2002).The Bitcoin option are different from Bitcoin futures that launched by a standard, well-regulated, matured and world-leading company like CME group, which are launched by some small exchange platform and Fintech start-up company. The option contract from different company is different, Deribit (Deribit, 2021, Options) and LedgerX (LedgerX,2021, Options) offer different contract specification and mechanism. The Bitcoin option pricing is sophisticated and still in research status, however, Stochastic Volatility with a Correlated Jump (SCVJ) model stand high in research estimation and interests and supported by many paper like Hou (2020), Nekhili (2020) and Ivan (2018). The application of Bitcoin option include protective put option strategy with Figlewski(1993) and Dunay (2018) as further reading. For collar options application, real world application from Adkins (2016) is a good example. The smart derivative contract that launched by ISDA with comprehensive detail legal guidance in different specific area (ISDA, 2019, 2020). The introduction and working mechanism are explained by Capco report (Capco, 2019). The example of Bitcoin OTC contract is atomic swap with example explanation (Miraz, 2019).

Bitcoin Futures

First, CME CF Bitcoin Reference Rate (BRR), a regulated daily reference rate of one Bitcoin in U.S. dollar as of 4 p.m. London Time (Bitcoin Overview – CME Group, 2021). Exchanges and trading platforms providing pricing data, including Bitstamp, Coinbase, Gemini, itBit, and Kraken. BRR are calculated based on the relevant transactions of all Constituent Exchanges. Calculation steps on any given calculation day are as follows: All Relevant Transactions are added to a joint list, recording the trade price and size for each transaction. The list is partitioned into a 12 of equally sized five minutes intervals. For each partition separately, the volume-weighted median trade price is calculated from the trade prices and sizes of all relevant transactions. A volume-weighted median differs from a standard median in that a weighting factor, in this case trade size, is factored into the calculation. The BRR is then given by the equally weighted average of the volume-weighted medians of all partitions (Introduction to Bitcoin Reference Rate – CME Group, 2021).

Bitcoin Futures contract (BTC) is a U.S. dollar cash settled and exchange-traded contract that based on BRR, enabling you to speculate on the future price of Bitcoin without holding the underlying cryptocurrency (no Bitcoin wallet or trading platform is needed), which is similar to equity futures. A cash settlement is a settlement method that the seller of the Futures contract does not deliver the Bitcoin but instead transfers the associated cash position on the settlement date. The Chicago Mercantile Exchange (CME) provides monthly cash settlement for Bitcoin futures, which enable futures owner can take cash rather than physical delivery. The Bitcoin Futures in CME group has a value of five times the value of the BRR (U.S. dollar per bit coin), with monthly contract listed for six consecutive months and two additional Dec contract months.   In the upcoming May 3, the CME group will launch Micro Bitcoin Futures, a smaller size (1/10 of one Bitcoin) Bitcoin Futures.

The CBOE Futures Exchange first introduce Bitcoin Futures in December 2017 that followed by CME group. However, since March 2019, CBOE stopped offering new contract. Instead of cash settlement, Bakkt offers physical delivery of Bitcoin. Bitcoin Futures Exchange for Physical (EFP) Transactions I only choose Bitcoin Futures in CME group for following description and

analysis. Bitcoin futures trading of central limit order through the CME Globex platform and clearing by CME ClearPort and CME Direct (Bitcoin Overview – CME Group, 2021).

Bitcoin Futures in CME group is regulated by the Commodity Futures Trading Commission (CFTC), the regulatory body with exclusive jurisdiction over US Bitcoin futures markets. The CME Bitcoin Futures is self-certificated with enhanced standard for oversight over the Bitcoin market and CFTC has limited statutory authority. The CME voluntary chose to give the CFTC the chance to review designated contract markets, derivatives clearing organizations (DCOs), clearing firms and individual traders involved in trading and clearing bitcoin futures. As an extension of this practice, the CFTC will engage in risk-monitoring activities with information sharing, in which it will request voluntary compliance by applicant derivatives exchanges with several criteria, including initial margins requirement, variation margin payment, size and development of the market, positions and changes in positions over time and open interest (CFTC Statement on Self-Certification of Bitcoin Products by CME, CFE and Cantor Exchange | CFTC, 2017).

To enter a Bitcoin Futures, an initial margin deposit and margin maintenance is required The Bitcoin Futures has bid/ask spread, the daily settlement happens between 14:59:00 and 15:00:00 Central Time. The profit or loss is immediately received or paid at the end of every trading day into or from your margin account. When closing the trade, a cash-settlement can close it. Each contract month settles to its volume-weighted average price (VWAP) of all trades that occur between 14:59:00 and 15:00:00 CT. If no trades occur on CME Globex between 14:59:00 and 15:00:00 CT, the settlement period, then the last trade (or the contract’s settlement price from the previous day in the absence of a last trade price) is used to determine whether to settle to the bid or the ask during this period. In the absence of any trade activity or bid/ask in a given contract month during the current trading day, the daily settlement price will be determined by applying the net change from the preceding contract month to the given contract month’s prior daily settlement price. As for the price limit, which is 20% above or below BRR normally, however, due to high volatility of Bitcoin, a special fluctuation limit at 7% above or 13% below.

Although, Bitcoin Futures seems like a FX Futures, they are totally different. FX Futures is a natural and well-developed contract have the option of physical delivery and physical underlying, low margin requirement, low volatility and low contract price that compare with cash-settlement only in Bitcoin Futures with no physical underlying, high margin requirement, high volatility and high contract price. 插图Moreover, they have different fair value pricing formula.  Normal FX Futures fair value pricing:

where  as spot exchange rate, r as base currency risk free rate and  as the foreign currency risk free rate.  As for Bitcoin Future fair value pricing:

]

Where  is spot Bitcoin price in U.S. dollar, r as the risk-free rate and d is Bitcoin cost of storage (Geman & Price, 2019). The Bitcoin cannot be viewed as a foreign currency, though, it has exchange rate with U.S. dollar, because risk free rate for Bitcoin is not exist. Therefore, Bitcoin is more like a commodity in fair value pricing. The situation here is the fair value of Bitcoin Futures are less than its quote price, hence, there exist an arbitrage.

The Bitcoin Futures effects on Bitcoin price. The research through the implied volatility of Bitcoin price shows that the Bitcoin market became immediately after the introduction of Bitcoin Futures, but the market gradually become more stable than it was before (Kim et al., 2020). The result is supported by (Shi, 2017) and other research reports. According to Kim et al. (2020), the volatility of Bitcoin Futures price decrease, when the contract approach to maturity.

The key benefits of the Bitcoin Futures: enabling the ability for investor and trader of an underlying cryptocurrency to hedge against future price volatility, and to speculate the market for profit earning. It is a great opportunity for price discovery in a transparent market. Easily trade without entry barrier around wallets and custody (insurance) of the assets. Trustable cash-settlement that based on regulated BRR (Bitcoin Overview – CME Group, 2021). The risk from counterparty almost zero by clearinghouse and regulation, no risk from hack or technical issues toward Bitcoin wallet (no wallet needed), low leverage mitigates the risk of liquidation and margin call when price drop, and limited price decrease the volatile of spot price.

Although Bitcoin Futures is a great mechanism that combine Bitcoin and futures contract, it has some drawbacks as well. The price limit may restrict the potential profit, especially price swing for Bitcoin price is common. The contract size is 5 Bitcoin that has a large contract value, result in a high margin maintenance requirement, which means the contract has high entry level and it is more suitable for institutional trading. The Micro Bitcoin Futures that will be launched might be a greater option for retail trading with relatively lower margin requirement.

Ether Futures

Ether Futures is U.S. dollar cash settle (ETH) and exchange-traded contract that based on ETHUSD_RR, enabling you to speculate on the future price of Bitcoin without holding the underlying Ethereum cryptocurrency (no Ethereum wallet or trading platform is needed). ETH went live on the CME group on February 8, 2021, which after Crypto Facilities (the U.K.) in 2018 and ErisX (the U.S.) in 2020. The following Ether futures only represent the contracts from CME group. Each futures contract is valued at 50 ether, which is defined by CME CF Ether Dollar Reference Rate (ETHUSD_RR) with pricing data from major cryptocurrency exchanges. The ETHUSD_RR, a daily reference rate that was designed by CME group and CF Benchmarks (benchmark administrator), which has same calculation method as BRR. The key benefits of

Ether Futures are easily managed price risk of ether cryptocurrency, transparent and regulated trading and price quotes, and regulated reference rate. The trading and clearing of Ether Futures is regulated by the CFTC with similar situation as Bitcoin Futures. Ether Futures share almost same characteristics as Bitcoin Futures and same fair value pricing method.

Bitcoin/Ether Futures Hedging Application

Bitcoin Futures and Ether Futures share the similar mechanism, the following application are all based on Bitcoin Futures.

Basic Short Hedge

Short hedge is a hedge, a short position in Bitcoin Futures contract, which is appropriate when the investor already own the Bitcoin and expects to sell it in the future date. Using Bitcoin Futures contracts to hedge against the drop of Bitcoin price in the future, due to its unpredictable price move and high volatility. 

The index level  here can also utilize Bitcoin Real Time Index (BRTI) that issued by CME group as the, however, BRTI is a real-time index that published once per second, 24 hours a day, 365 days per year without daily closing price. Therefore, BRR is chosen which announced once a day and have the same calendar as Bitcoin Futures.

Simple hedge ratio:

The hedging problem is the investor owns 100 Bitcoin and want to hedge against the price drop of Bitcoin in two weeks. Since the underlying asset of Bitcoin Futures is the same as the asset being hedged, the hedge ratio: h = 1 that mention in Hull’s. The hedge ratio is the ratio of the position taken in futures contracts to the size of the exposure. The number of futures contracts to hedge the Bitcoin position:

Assume that the Bitcoin BRR movement follow the Bitcoin price volatility index and there are three situations:

Gain/Loss of Bitcoin Futures contract at maturity date:

Date4/9/2021
Bitcoin BRR=58347.48
Interest Rate5.10%
Dividend Yield0.00%
Maturity Date4/21/2021
Days to Maturity12
Futures Price Quote=58,760.00
Futures Fair Value58446.67
Futures multiplier= m5
Bitcoin Fund to Hedge ($)=5834748.00
Number of futures= N20
Bitcoin price volatility=3.24%

Table.2, basic information

Simple hedgeBRR StationaryBRR RisesBRR Falls
Bitcoin BRR at maturity date=58347.4860237.9456457.02
Bitcoin Fund at maturity date=5834748.006023793.845645702.16
Settlement Futures price=58347.4860237.9456457.02
N (unchanged)202020
Gain/Loss on Bitcoin0.00189045.84-189045.84
Gain/Loss Futures41252.00-147793.84230297.84
Gain/Loss on Bitcoin hedge with futures41252.0041252.0041252.00
Final Portfolio Value5876000.005876000.005876000.00

Table.3, basic short hedging with simple hedge ratio performance

Optimal hedge ratio:

When the object of the Bitcoin hedge is minimizing variance, the optimal hedge ratio should be utilized and hedge ratio of 1 is not optimal in this situation. The Bitcoin Futures contracts has the characteristic of daily settlement, therefore, a series of one-day hedge is necessary. Define:

 one-day percentage changes of BRR, during a period equal the life of the hedge

 One-day percentage changes of Bitcoin Futures, during a period equal the life of the hedge

When the investor is long the Bitcoin and short Bitcoin Futures, the change in the value of the investor’s position during the life of the hedge,  is:

The variance of

Therefore, using first derivative to find minimum of :

And setting it equal to zero, we find the value of h that minimize the variance is:

The  and  are historical data that has the same time series as the life of Bitcoin Futures.

Optimal Hedge 
 0.021
 0.026
ρ0.882
h0.694
Number of futures= N*14

Table.4, basic information

Optimal HedgeBRR StationaryBRR RisesBRR Falls
Bitcoin BRR at maturity date=58347.4860237.9456457.02
Bitcoin Fund at maturity date=5834748.006023793.845645702.16
Settlement Futures price=58347.4860237.9456457.02
N* (unchanged)131313
Gain/Loss on Bitcoin0.00189045.84-189045.84
Gain/Loss Futures26813.80-96065.99149693.59
Gain/Loss on Bitcoin hedge with futures26813.8092979.84-39352.24
Final Portfolio Value5861561.805927727.845795395.76

Table.5, basic short hedging with optimal hedge ratio performance

Calendar Spreads Hedging

Calendar spread strategy, the hedger can simultaneous entering a long and short position on the Bitcoin Futures, however, with different maturity month to be filled at specific price difference between the contracts. The strategy is the outcome of finite lifetime of futures contract and a property that periodically forces both near term and long-term investor to exchange their contracts with different maturity date.

The hedging problem is the investor want to buy 100 Bitcoin in seven months later, because of currency shortage to cover 100 Bitcoin now (August 1,2020) and afraid of Bitcoin surge in the future (April). The strategy is maintaining a long Bitcoin Futures on Bitcoin over six months. Although Bitcoin Futures in CME group has listed six consecutive months and two additional Dec months (if Dec in consecutive months, then only one additional Dec), it only list until March (Oct, Nov, Dec, Dec (additional), Jan, Feb, March). Moreover, there exist risk of liquidity for the contracts beyond six months. In such case, a roll-over hedge is necessary, which is a type of calendar spread. Firstly, long a one-month Bitcoin Futures, and then close the futures contract near the maturity and long another Bitcoin Futures that expire in one month later to roll the position over just prior to each delivery month. One-month futures contract for hedging is the most liquid choice.

The number of hedging futures contracts, N,  is calculated through simple hedge ration method.

Futures PriceInitial=Close=Open=Gain/Loss in futures=
Oct, i=1106451347913845283400
Nov, i=2 1373516628-11000
Dec, i=3 1973023685310200
Jan, i=4 37242348551355700
Feb, i=5 47002463251214700
March, i=6 5334654060702100
April, i=7 58760 470000

Table.6, calendar spread hedging monthly information

Buy Bitcoin Date=4/9/2021
BRR=10623.33
Bitcoin Fund Cost at =-1062333
m5
N20
Initial futures cost-212900
Bitcoin BRR at =58347.48
Bitcoin fund cost =-5834748
Gain/Loss in all futures4325100
Bitcoin fund net cost-1722548

Table.7, calendar spread hedging with simple hedge ratio performance

The Bitcoin price increase from $10623.33 to $58347.48, and hedger receives $4325100 compensation for price surge. Although the cost of buying Bitcoin has 4.5 times the original one, only 1.6 times after hedging.

Bitcoin Options

The Bitcoin Option Trading in the U.S. is legal since CFTC approved and issued LedgerX for Derivatives Clearing Organization (DCO) on October 2, 2017. LedgerX is a digital currency options and futures exchange and clearinghouse that regulated by CFTC. The Bitcoin Mini Option offered by LedgerX is a European style that the option exercise only at expiration.  The contract size is 0.01 Bitcoin, and trading hours is 24 hours per day and seven days per week (Options, 2021). The settlement in LedgerX is physical-settled and there is no auto-exercise, where investor should submit exercise instrument on the platform. More detail, trader determined whether that option is in the money, at the money or out of the money, which means they can factor in different exchanges and different benchmarks for underlying Bitcoin price. Therefore, platform do the delivery of the trade and cannot manipulate for profit through determine whether Bitcoin price hit the strike price and give trader more flexibility and determination. When investors exercise long call options, they should have enough US dollar that deposited on the platform to buy Bitcoin at the U.S. dollar strike price. As for long put options, investors are required to have enough Bitcoin on the platform to sell Bitcoin at the U.S. dollar strike price. Closing out of a position is available any time before expiration, which means investors can close a short position by purchasing the number of option contracts that they are short or close a long position by selling the number of option contracts that they are long. When execute close out of short position, the position will be zero and position locked collateral for previous short position will be closed. And when execute close out of long position, no short collateral is required. The Chief Operation Officer of LedgerX said that people like miner who owe Bitcoin are exposure to the risk of U.S. dollar versus Bitcoin can hedge directly through pledging it directly or selling it, rather than convert it to dollar then use dollar to hedge (Shin, 2019). The option is a great and helpful tool for who in their consumer-facing or merchant-facing business that have bitcoin on their balance sheet to hedge their risk on their balance sheet, which are similar to large oil producers or refinery do. Another characteristic is Bitcoin Option is negotiated trades that people propose a price and size and show the trade on the exchange, all of fully collateralized options are centrally cleared by the LedgerX clearinghouse. Therefore, there exist bid/offer for exchange.

There exists lots of difference between Bitcoin Options and other FX options. The price of Bitcoin Options contact is far more expansive than FX option contact price. The reason is Bitcoin has higher implied volatility than FX rate which means a higher price or more expensive the premium is likely to be.

Unregulated Bitcoin Option exchange that provided by Derbit. After LedgerX, OKEx launched options trading on December 27, 2019.

Deribit has dominant Bitcoin Option market share since 2016 when the company come to exist, and it has different characteristic as Bitcoin Option in LedgerX. In Deribit, the Bitcoin Option is cash-settlement that the options writer will pay any profit due to the holder rather than transferring asset. The underlying is Deribit BTC Index, however, when there exist a corresponding future has same day as expiration that futures price will be used. The order size that greater than 0.1 option contract is allowed. The order can be filled, and price can be determined through BTC or additional advanced order type (U.S. dollar and implied volatility) at trader’s preference. The price of the option in order book is priced at BTC, which means the option price equal how many Bitcoin. If options expired in the money, the exercise is automatic with cash settlement in the equivalent of Bitcoin.

Bitcoin Option Pricing

The pricing model used here is Black-Scholes model. There exists more advanced pricing model Stochastic Volatility with a Correlated Jump (SVCJ) model with numerous paper and research prove its suitable for Bitcoin option pricing, because option prices are strongly driven by jumps in the returns and volatility process of Bitcoin (Chen et al., 2018). Moreover, Kou Jump-Diffusion model shows the goodness of fit, but there is no significant difference with Black-Scholes model (Silva, 2018). Bitcoin price itself does not follow the lognormal pattern with excess kurtosis. Although Black-Scholes model is not the perfect choice for Bitcoin option pricing, we still use here as a benchmark pricing model for at the money option. Furthermore, the characteristic of Bitcoin option has broken some limits: no dividend payout and no early exercise.

Assume Bitcoin price has the lognormal distribution and follow the random walk property (geometric Brownian motion with constant drift and volatility), there exist no transection cost and no arbitrage opportunity, ability to borrow and lend any amount at risk free rate and buy and sell any amount of Bitcoin and having risk free rate.

Black-Scholes model pricing formular:

Where N(x) function is the cumulative probability distribution function for a variable with standard normal distribution. K is the strike price of options, r is the risk-free rate that quotedfrom U.S Treasury daily yield curve rate, T is maturity date and t is the options trading

date,  is the Bitcoin price at trading date and  is the volatility of Bitcoin price. The volatility here can be quoted from Bitcoin volatility index that depend on the exchange platform where offer the option trading.

Every exchange platform that provides Bitcoin option trading service have its own pricing model that supported by risk management team, therefore, the quoted price and implied volatility that obtained from Black-Scholes model are different. Another pricing method Binomial tree risk neutral model, when using sufficient number of steps, the price obtained from Binomial tree is identical to the Black-Scholes model.

Bitcoin Options hedging application

Protective Put Option

Traditionally, when investor hold underlying asset, long a put option is useful to hedge against the price decrease of underlying asset that is based on investor bearish on the asset. However, when Bitcoin as the underlying asset, the price of Bitcoin in the long term is bullish. Due to Bitcoin high volatility and sometimes plummet in a short time, a protective put hedging strategy is attractive when it comes to Bitcoin hedging. The potential goals why an investor might choose the strategy are limiting risk when holding Bitcoin and guard against previously purchased Bitcoin to hedge against short term uncertainty and potential loss, without sacrificing a majority of potential increase. The strategy is hold a position in Bitcoin and long put options with strike price that similar the current price of Bitcoin.

The hedging problem is the investor hold 100 Bitcoin and what to hedge against unexpected price fall in the following week, but still bullish the Bitcoin price trend in the future.

The payoff and P/L from protective put that based on initial Bitcoin price, Bitcoin put option premium paid, strike price and underlying price at maturity date.

Protective Put Portfolio 
Trade date4/15/2021
Strike price= K62000
Maturity date4/23/2021
Bitcoin put option premium= P1340.50
Underlying Bitcoin Price at trading date= 63831.05
Implied volatility= IV59.40%
Risk free rate1.64%
Multiplier= m1
Number of Bitcoin= n100
Number of put option= N100
Number of put option (delta hedging) =263
Delta of Bitcoin=1
Delta of put option=-0.349

Table.8, protective put hedging strategy basic information

Simulate 11001 situations that Bitcoin price on April 4, 2021 that range from $55000 to $66000.

Fig.1, protective put payoff vs Bitcoin position payoff

The maximum profit for Protective put strategy is infinite, which is only reduced by the fixed amount of put options premium paid (relatively expansive that compare to other underlying assets options). The maximum loss is limited, once future Bitcoin price below the strike price will be compensated by the put option profit.

As for the delta neutral hedging in protective put, which enable the Bitcoin position to continue to profit if the Bitcoin price rises or falls strongly. Especially when price fall dramatically, the portfolio can gain infinite profit that compare with limited and fixed loss if normal hedging. Although the maximum profit is infinite, the premium cost increase that due to the more contracts required to delta neutral hedging than normal hedging which limits the profit. Therefore, there exists lower and upper breakeven price, when price above upper price and lower

than down price, the portfolio can make profit. Because delta neutral hedging consist of neutralize the move in option price and Bitcoin price, which requires rebalancing number of option contracts constantly to avoid being over or under hedged. When using Black-Scholes pricing model as a benchmark, the

Fig.2, protective put payoff vs Bitcoin position payoff with delta neutral hedging

To obtain a better understand of protective put strategy work in different trending environment, simulated and analyses the path of bitcoin through geometric random walks. 1000 simulations were used for three different scenarios with portfolio and Bitcoin returns were calculated as output. Using the past 111 days of Bitcoin historical natural log-return and then calculating the drift of value 0.0116 that based on the average of log-returns with volatility incorporated. With positive drift, the trend of simulated price goes up and unhedged Bitcoin position has a better average return which makes the hedge less necessary. For the negative drift, -0.0116 was used

that is the negative counterpart of the value in positive drift random walk. The drift implied a downward trend of Bitcoin price and a better average return in hedged portfolio.

drift0.01160.0000-0.0116
σ4.67%4.67%4.67%
4/15/2021=63831.0563831.0563831.05
4/16/2021=64506.5563761.6563025.29
4/17/2021=65189.0964436.2662229.75
4/18/2021=65878.7965118.261444.18
4/19/2021=66575.9365807.0760668.47
4/20/2021=67280.4666503.4459902.54
4/21/2021=67992.3667207.1359146.35
4/22/2021=68711.8167918.3158399.71
4/23/2021=69438.8668636.9857662.48
 69439.1168637.2157662.25
Average portfolio return6.55%5.32%-4.87%
Bitcoin return8.79%7.53%-9.66%

Table.9, simulations and protective put hedging performance

Collar hedging strategy:

Collar option hedging strategy is employed to decrease both negative and positive return of Bitcoin, which hedge against potential volatility of Bitcoin price. The collar position is composed of holding the Bitcoin position, longing out of the money put option contracts and shorting out of the money call option contracts. More conveniently, a combination of using protective put option and covered call option.

Collar 
Today4/23/2021
Bitcoin price underlying=50042.59
Number of Bitcoin= n100
Bitcoin position5004259
Put option premium=1376.19
Put option maturity date4/30/2021
Put option strike price=48000
Put option implied volatility=0.888
Number of put option contracts=100
Call option premium=1326.14
Call option implied volatility=0.793
Call option maturity date4/30/2021
Call option strike price=52000
Number of call option contracts=100

Table.10, collar option hedging strategy basic information

Fig.3, collar option payoff vs Bitcoin position payoffs vs protective put option payoff

By taking a long position in OTM put option and short position in OTM call option, when price drop below the put option strike price, the compensation from options aggregate, when price rise above the call option strike price, the loss from options aggregate. If the value of Bitcoin price between two strike prices, the loss experienced by put option offset by gain from call option. In the chart below, the price below the and above  the payoff is flat with limit potential downside and upsize, and between the strike price the payoff almost same as payoff of Bitcoin position.  The strategy allows covered call option sold to cover the cost from protective put option, and still allows potential upward of Bitcoin price and protect against large loss. On April 23, 2021, Bitcoin price has experienced a dramatically drop, which has high down-size risk with low probability uptrend in the short-term but a strong long-term potential. In this situation, an almost free cost hedging strategy is more attractive to hedger. When it compared with protective put, the hedger can benefit from collar strategy that has lower cost, more price downward compensation and lower breakeven price.

The investor holds 100 Bitcoin and decided to hedge through Collar hedging strategy, who has experienced one-week continuous price decline and afraid of further huge price drop. The number of put option contracts and call option contracts are same and calculated by the same method as protective put. Simulation of future Bitcoin price shares the same method as protective put option. Using past two weeks average log-return with standard deviation incorporated as drift that represent current Bitcoin price trend. It is obvious that simulated Bitcoin price in downward trend with drift value of -0.0093.

drift-0.00930.00000.0093
σ0.032160.032160.03216
4/23/2021=50042.5950042.5950042.59
4/24/2021=49555.4150016.6750482.22
4/25/2021=49073.0449990.850925.75
4/26/2021=48595.3149964.9551373.12
4/27/2021=48122.2849939.1451824.47
4/28/2021=47653.8249913.2952279.78
4/29/2021=47189.9549887.5552739.13
4/30/2021=46730.6249861.8253202.49
=46730.7549861.7653202.57
Average portfolio return-4.18%-0.46%3.81%
Bitcoin return-6.62%-0.36%6.31%

Table.11, simulations and collar option hedging strategy performance

OTC Bitcoin market

The Over the Counter (OTC) Bitcoin market acts as an alternative to exchanges, which is another less formal method to trade Bitcoin and its derivatives (also NFT). OTC has no exchange as market maker between buyers and sellers and connects them directly. There is no physical location, buyers and sellers should communicate through forums, chatrooms, telegram, LinkedIn, or OTC broker, etc. People who want to trade Bitcoin or its derivatives will quote the prices they wish to sell or buy. According to Bloomberg reported that the daily cryptocurrency OTC has $15 billion market size that compared with $250 million to$30 billion per day in total OTC market size (Kharif, 2018). Today, the generally daily OTC volume for cryptocurrency is much larger than exchanged volume, for example Circle said OTC market is three times the regular exchanged and Aite group’s research showed that 65% of trading volume happen in the OTC market. The first OTC Bitcoin market is Circle, which was launched because miner need a place to sell large amount of mined Bitcoin immediately. The miner as the main seller in OTC market and hedge fund as main buyer, and sometimes regulated broker-dealer or exchange OTC desks involved (Editorial Team, 2019).

There are some advantages why people or institutions prefer OTC marker for trading. Increasing liquidity: cryptocurrency exchanges have low liquidity; however, OTC market provide opportunity for large trading orders of cryptocurrency quickly. Price protection: trading in OTC market even in large amount does not impact the cryptocurrency’s price (except news dissemination about large amount trading), and no slippage (executed price distinct from expected price). Anonymity: different from trading in exchange platform that easy to track, order in OTC desk does not show up. No amount limitation: the majority exchange platform limit trading and withdraw per day. More token varieties choice: there are limit choice of cryptocurrency, derivatives, tokens, NFT or smart contracts for trading.

The disadvantages are obvious. Settlement risk or counterparty risk: limit deliver, or cash payment guaranteed (especially when large order happened) and not all OTC brokers offer custody solutions. Missing regulation: even though some OTC brokers and desk are regulated, when compare with exchanged-trading platform is not enough and most of OTC market is unregulated. Today, emerging software such as Caspian, OTCXC and Fidelity are launched to protect institutional or single users to securely trading in OTC market.

Swap

Atomic swap: crypto-to crypto swap, exchanging one type of cryptocurrency to another (exchange Bitcoin to Litecoin). A peer-to-peer trades across different blockchain of different cryptocurrency, which allows people to exchange their coins directly from their wallet without

third party participated that based on smart contracts. The key technology and algorithm is Hash Timelock Contracts (HTLC). Hashlock and Timelock form the HTLC, which create a trust rule between two counterparties that prevent executing partially. A example can easily explain how Hashlock works. Institution A deposit Bitcoins into a contract address that works like a , and at same time generate a key to the . Then A share the cryptographic hash of key to the institution B, but B cannot open the safe now. B uses the hash that offered by A to create a to store Litecoins. To claim Litecoins, A can use the real key to open the  that has the same hash as , meanwhile, A reaveals the real key to B and B can get access to  at the same time. The Hashlock is what prevent either parties to access counterparties’ fund without key or data revealed (’s key).

The main advantage of atomic swap are utilizing decentralized characteristic that cryptocurrency have that two parties do not need to offer their wallet or funds to exchange or third party. The trading happens quickly and has almost zero trading fees and operational cost. Furthermore, altcoins can also exchange with each other without using Bitcoin as an intermediary cryptocurrency.

Smart derivative contract

There are numerous possible definitions for smart derivative contract and one of the best definitions according to Legal Guidelines for Smart Derivatives Contracts: Introduction published by ISDA in 2019 is: a smart contract is a contract which include automatically performed computer code in pre-defined condition and some may require human input and control. It is an efficient derivative that incorporated with computer code which are automatically and irreversible. When it comes to risk management purpose, the industry participants will retain human involvement (Legal Guidelines for Smart Derivatives Contracts: Introduction – International Swaps and Derivatives Association, 2019). The potential benefits the smart contract provide to people are better regulation, reduced complexity and cost, and increased efficiency. The market participant following the same frame and automatically working, which decrease the time cost that required to negotiate contracts.

The smart derivative contracts are being used in the near term. ISDA published a series of Legal Guidelines for Smart Derivatives Contracts: Foreign Exchange Derivatives, Credit Derivative, and Interest Rate Derivatives. The purpose of these guidelines is to support smart derivatives contracts developers and other main stakeholder through explaining the core principles of ISDA documentation and raising awareness of the important legal and regulatory issues they should consider when developing and deploying such solutions within the derivatives market.

Moreover, the guideline identifies the potential application of such technology to the specific market. ISDA first proposed a standardized solution (or common language) Common Derivatives Model (CDM) in 2017, providing market participant a lifecycle common digital representation in derivative trading. Barclays is the first institution making blockchain application in reality through CDM. The Distributed ledger technology (DLT) is one of the key parts of smart derivatives contracts. In essence, DTL provide data and record that available for all participants with only one centralized record of data. Only unanimous agreement among all parties can change record in DTL. In smart derivative contract, DTL can restrict access to only participant and regulators. The DTL contribute to bind participants and help them dealt complexity among automatically derivative trading and data collection (What Is the ISDA CDM? – International Swaps and Derivatives Association, 2018).

Summary and Further Suggestions:

From this report, we realized the popularity and growing attention toward cryptocurrency especially Bitcoin and Ethereum. The high volume of cryptocurrency trading and exchange promote the flourish and gradually mature of Bitcoin derivative and Ethereum derivative in exchange-trading and OTC markets. The standard platform, contract and regulation and law involved has become normal situation in cryptocurrency market. Moreover, Rollover futures hedging, protective put and collar option hedging that frequently utilized in traditional derivative hedging area are proved workable and helpful in hedging cryptocurrency. The cryptocurrency futures fair value pricing and Black-Scholes model in option pricing could be viewed as a benchmark price. The successful application of cryptocurrency derivative will arouse investors and hedgers’ attention and interests, which will increase investment, research and development in derivatives. OTC market since it appeared, Bitcoin derivative contracts and other altcoin derivative contracts are well-developed. With the launch of smart derivative contract, the ISDA offers participants a standard language for future cryptocurrency OTC derivative development.

Studying and research of cryptocurrency derivative has a long way to go, especially since cryptocurrency owns different characteristics that compare with traditional commodity, foreign currency or equity as underlying asset. When it comes to derivative pricing, there not exit a popular and generally accept pricing methods like Black-Scholes model, and pricing model that designed for traditional asset may not be suitable for cryptocurrency derivatives, new and advanced pricing model and valuation method required more researchers’ attention and effort. And the launch and development of derivative may have impact on price, return and volatility of underlying asset, a few reports talked about the question and need more research to prove it.

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