1. CME Bitcoin Futures: Volatility and Liquidity

2. Introduction
This paper explores empirically the behavior of the Chicago Mercantile Exchange (CME) bitcoin futures contract.
The analysis focuses on the time period between the launch of the CME bitcoin futures contract on December 18, 2017, and September 17, 2018.
The behavior of the bitcoin spot market and CME futures market is compared and analyzed along several dimensions:
price,
volatility
liquidity.

3. Bitcoin Overview A form of electronic cash A decentralized currency
Based on open-source software
Could be exchanged for other currencies, products, and services
Not subject to central bank or governmental control
CME Bitcoin Futures began trading December 18th, 2017

4. The Bitcoin Spot Market
Bitcoin allows peer-to-peer transactions based on a distributed ledger technology known as Blockchain.
Bitcoin uses a decentralized database where peer-to-peer transactions are broadcast to a network of users.
The transactions are validated by network nodes, miners.
The transactions, or blocks, are recorded in the ledger and linked to the previous version of the ledger to form a chain of transactions.

5. Market Size December 2017 through September 2018
Cash Market Capitalization
MEAN: $ 7,269,052,303
MEDIAN: $ 5,864,454,912
MAXIMUM: $ 23,840,899,072
MINIMUM: $ 2,923,670,016
CME Futures Market Volume
MEAN:
MEDIAN:
MAXIMUM: 11,533
MINIMUM:
CME Futures Market Open Interest
MEAN:
MEDIAN: 252
MAXIMUM: 2460
MINIMUM:

6. CME Bitcoin Futures Implied Notional Values
CME Futures Contract Closing Price
MEAN: $8796
MEDIAN: $8135
CME Futures Market Volume
MEAN: 967
MEDIAN: 87
CME Futures Market Open Interest
MEAN: 607
MEDIAN: 252
Implied Notional Values:
MEAN: x 607 x $8796 = $26,695,860
MEDIAN: 5 x 252 x $8135 = $10,250,100

7. Chicago Mercantile Exchange Bitcoin Futures Market
The Chicago Mercantile Exchange (CME) lists and trades the futures contract on an aggregate index of bitcoin spot prices.
On December 18, 2017, the Chicago Mercantile Exchange (CME) launched its bitcoin futures contract. Table 1 provides its salient features.

8. Table 1: Salient Features of the Chicago Mercantile Exchange Bitcoin Futures Contract

9. Price Trend
Figures display the movements of the bitcoin spot and nearby futures prices during the study period.
The peak bitcoin price was observed on December 17, 2017, a day before the CME bitcoin futures contract was introduced.
Since then, both the spot and futures prices declined in a close, tight relationship.
The reason for this steady downward movement in bitcoin price was attributed to the short-selling opportunities made available via futures trading.

10. Figure 1: Closing Cash Price

11. Figure 2: Closing Futures Price (Bitcoin)

12. Figure 3: Daily Closing Prices of Bitcoin Futures and Bitcoin Spot (12/18/2018-09/17/2018)

13. Table 2: Descriptive Statistics for Daily Bitcoin Futures and Bitcoin Spot Price, Volume and Open Interest (12/18/ /17/2018)

14. Liquidity
We examine the relative market sizes of the bitcoin spot and futures to analyze the relative liquidity of the futures market to the spot market.
We measure the size of the spot market,
by dividing the spot market price times number of coins traded, by the daily closing bitcoin spot price to obtain the number of bitcoins
We measure the size of the futures market,
by multiplying the daily trading volume by 5 because the size of the CME bitcoin futures contract is five bitcoins.

15. Figure 4: Daily Trading Volume of Bitcoin Futures and Bitcoin Spot in Number of Bitcoin (12/18/ /17/2018)

16. Liquidity Ratio The ratio of trading volume to open interest
is a more appropriate liquidity measure
because it focuses specifically on the trading activity that creates and supports open interest.
A large ratio means that trading volume is large enough to support the willingness of the traders to carry an open position overnight or longer.
This ratio can be small in a well-established market, because open interest is often much larger than the trading volume.
The large open interest, being associated with a large hedging demand and use, is often found in a well-developed futures market.

17. Figure 5: Liquidity Ratio of the Ratio of Daily Volume over Daily Open Interest in Bitcoin Futures (12/18/ /17/2018)

18. Table 3: The Liquidity Ratio of Daily Trading Volume over Open Interest for Selected Futures Contracts (12/18/ /17/2018)

19. Volatility 𝜎 2 =.5(𝑙𝑛 𝐻𝐼𝐺𝐻 𝐿𝑂𝑊 )2 - .39(𝑙𝑛 𝐶𝐿𝑂𝑆𝐸 𝑂𝑃𝐸𝑁 )2
Garman/Klass Extreme Value Method
𝜎 2 =.5(𝑙𝑛 𝐻𝐼𝐺𝐻 𝐿𝑂𝑊 ) (𝑙𝑛 𝐶𝐿𝑂𝑆𝐸 𝑂𝑃𝐸𝑁 )2
Where: HIGH denotes the highest price observed during the trading day;
LOW denotes the lowest price observed during the trading day;
OPEN denotes the opening price at the beginning of the trading day;
CLOSE denotes the closing price at the end of the trading day.

20. Volatility CME Futures Market Annual Volatility Garman Klass
MEAN:
MEDIAN:
MAXIMUM
MINIMUM
Daily Volatility Garman Klass
MEAN:
MEDIAN:
MAXIMUM
MINIMUM

21. Volatility Cash Market Annual Volatility Garman Klass
MEAN:
MEDIAN:
MAXIMUM
MINIMUM
Daily Volatility Garman Klass
MEAN:
MEDIAN:
MAXIMUM
MINIMUM

22. Table 4: Descriptive Statistics of the Garman-Klass Annualized Volatility (12/18/2018-09/17/2018)

23. Figure 6: The Garman-Klass Annualized Volatility of Bitcoin Futures and Selected Futures Contracts (12/18/ /17/2018)

24. Table 5: Pearson Product-moment Correlation Coefficients of the Garman-Klass Annualized Volatilities (12/18/ /17/2018)

25. Changing Bitcoin Volatility in Three Separate Periods
We used the graphs in Figures 3 and 4 to identify what appears to be a regime shift in the bitcoin market volatility after April 1, 2018.
We examine the regime shift by dividing the data into two subperiods:
December 18, 2017 through March 31, 2018,
April 1, 2018 through September 17, 2018.

26. Regression Analysis, Bitcoin Futures Volatility =f(Bitcoin Spot Volatiltiy)
𝜎 𝑡 𝐹 = 𝛼+ 𝛽 𝐹 𝜎 𝑡 𝐶 + 𝑒 𝑡
𝜎 𝑡 𝐹 represents the square root of the Garman-Klass variance for the nearby bitcoin futures price,
𝜎 𝑡 𝐶 denotes the square root of the Garman-Klass variance for the bitcoin spot price at time t with i.i.d errors of 𝑒 𝑡 .

27. Table 6: Simple Regression Output of Bitcoin Futures Price Volatility on Bitcoin Spot Price Volatility
Standard errors in parentheses
* p<0.05, ** p<0.01, *** p<0.001

28. Figure 7: Rolling Window Coefficient and Correlation Coefficients between Volatilities of Bitcoin Futures Price and Bitcoin Spot Price (Window Size = 50 Trading Days)

29. Bitcoin Volatility Relationships to Other Futures Market Volatilities
We use regression analysis for the three periods to examine the robustness of the relationship between the bitcoin futures price volatility and the price volatility of other futures contracts:
E-mini S&P 500,
Gold,
10-year T-Note,
Euros,
Crude Oil.

30. Regression Analysis Bitcoin Futures Volatility =f(Selected Futures Contracts Volatilties)
𝜎 𝑡 𝐹 = 𝛼+ 𝛽 𝑖 𝜎 𝑡 𝑖 + 𝑒 𝑡
𝜎 𝑡 𝐹 represents the square root of the Garman-Klass variance for the nearby bitcoin futures contract,
𝜎 𝑡 𝑖 denotes the square root of the Garman-Klass variance for the established futures contract i at time t with 𝑒 𝑡 as errors.
i represents one of the following futures contracts:
E-mini
S&P 500
Gold
10 Year T-Note
Euros
Crude Oil.

31. Table 7: Cochrane-Orcutt autoregressive estimation output of the daily volatility of bitcoin futures on alternative financial futures

32. Margins and Price Limits
As of December 12th 2017, and subject to change,
The Maintenance Margin for the BTC future is 43%,
The Initial Margin for Hedger is 100% of the maintenance margin
The Initial Margin for Speculator is 110% of that number, or 47.3% .
Bitcoin futures will be subject to daily price fluctuation limits of 7%, 13% and 20%. These limits apply to both upside and downside price changes relative to the prior day’s Bitcoin futures settlement price. 

33. Margins and Price Limits Examples
September 17, 2018
Buy 1 December Bitcoin Futures contract at $6,230.
Position Notional Value:
1 Contract for 5 $6,230 = $31,150
Margin:
Maintenance: .43 of $31,150 = $13,394
Initial: 1.1 x .43 = .473 of $31,150 = $14,734

34. Margins and Price Limits
The difference between the initial margin and maintenance margins is 4.3% of the notional value of $31,150.
This is well below the daily price limit of 7%
Means the exchange’s maintenance margin can work well in periods of normal volatility.
The initial margin of $13,394 which is equivalent to $2, per bitcoin is very similar to the price movement of one standard deviation of $2, as observed in Table 2.

35. Brokerage Margins
Brokerage firms decided to set their own customer margins for Bitcoin futures far above those set by the exchange
Due to the extreme price volatility observed in the bitcoin spot market in 2016 and 2017,
For example, the margin requirements for a speculative account at a prominent futures brokerage firm based in Chicago were
110% of notional value for initial margin and 94% of notional value for maintenance margin.
In addition, the brokerage firm required an account balance of $250,000
Only allowed open positions in 3 bitcoin futures contracts.
When the notional value of a bitcoin futures contract is $31,150
A customer must post an initial margin of 1.1 times $31,150 which equals $34,265.
The maintenance margin is 0.94 of $31,150 which equals $29,281.
Given that one standard deviation of bitcoin futures price is $2,621.91, which is $13, per contract,
the initial margin of $34,265 per contract can cover 2.6 standard-deviation movements in bitcoin futures price, which corresponds to an approximately 99.5% of all price movements.

36. Conclusions
Bitcoin cash market is much deeper than the CME Bitcoin futures market
Bitcoin cash market and CME Bitcoin futures market price behavior is similar
Bitcoin cash market and CME Bitcoin futures market annualized median price volatility is similar ≈.65
The Bitcoin futures market volatility is systematically higher than the
Bitcoin cash market volatility
Selected CME futures contracts
Based on the Garmon Klass daily volatilities the brokerage Bitcoin futures margin percentages should be reduced to encourage more trading activity and to increase liquidity.