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**Table of contents**

- PRICING AND SETTLEMENT
- Trading Bitcoin Futures with IBKR | IB Knowledge Base
- Cboe Abandons Bitcoin Futures
- How Are Bitcoin Futures Different?

As such, the question as to whether the cost-of-carry approach is an appropriate one for pricing cryptocurrency-based futures has not been established, but can be addressed via various tests including cointegration, lead-lag causality and price discovery stability. Given some of the unique features of cryptocurrency spot and futures prices summarized in the Introduction, one might expect some differences in the cryptocurrency futures pricing model compared to other asset markets.

Place this in a world of disruption coming from e. The nature of the data used and econometric flexibilities employed are discussed in Section 3 below. BRR refers to the daily reference rate of the U. The BRR aggregates the trade flows from the major Bitcoin spot exchanges, for example, Bitstamp, Coinbase, itBit and Kraken at 4 pm London time to ensure transparency and replicability in the underlying spot markets.

### PRICING AND SETTLEMENT

We switch the most nearby contract to the second most nearby one if the trading volume of the former is exceeded by the latter at the former's contract month. The Gemini auction price and the BRR are used to represent the spot markets under consideration in this paper. After matching the spot and futures data series, we are left with observations for the CME sample and observations for the CBOE sample.

Note that our sample excludes data on weekends due to unavailability. Both the spot and future prices are downloaded from Thomson Reuters Datastream for our empirical analysis. It should be noted that the futures and spot prices used by the CBOE and CME are different, hence the empirical analysis is based on the counterpart spot markets.

All spot and futures prices are transformed to natural logarithms and are presented as Fig. As can be seen from the figure, there is a decreasing trend for both spot and futures prices from the beginning of the sample period until the early of February , which might represent a bear market in both the spot and futures markets. From early February , both prices follow an upward trend until the end of sample period, which suggests a bull market.

Second, the patterns of both spot and futures prices look similar. It is possible that there exists a long run relationship between spot and futures prices. This will be further examined formally via tests for cointegration.

We also provide descriptive statistics on Bitcoin spot and futures daily returns in Table 2. As can be seen from the table, the means of spot and futures returns are negative. The volatilities of the four markets are similar. Second, returns of the four markets do not follow a normal distribution as indicated by a Jarque-Bera test.

This might be due to non-zero skewness and excess kurtosis, which will be further examined via a semi-nonparametric SNP approach.

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Finally, heteroscedasticity may exist in the spot and futures returns given the existence of significant Ljung-Box Q statistics. The volume of CBOE Bitcoin futures dominates in the early markets from December to the middle of after which the CME's product starts to dominate in the market and this phenomenon becomes more evident when the CBOE decided to stop listing its product in March Thus it is interesting to investigate the pricing behaviour of futures contracts in these two markets resulting from those transactions.

Daily returns are calculated as the first order differences of log daily prices. JB , the Jarque-Bera test statistic for normality. LB 2 12 denote the Ljung-Box Q test statistic for return squares up to lag order The following section is taken from Shi et al. We can write an unrestricted VAR p in multi-variate regression format simply as:. In order to test the null hypothesis that y 2 t does not Granger cause y 1 t , the Wald test for such restrictions can be denoted as:.

Each row picks one of the coefficients to set to zero under the non-causal null hypothesis. There are p coefficients on the lagged values of y 2 t in Eq. Following the recent bubble detection tests of Phillips, Shi, and Yu [] , Shi et al. If the Wald statistic sequence exceeds its corresponding critical value, a significant change in causality is detected.

The origination termination date of a change in causality is identified as the first observation whose test statistic value exceeds goes below its corresponding critical values. This is known as the recursive evolving procedure. Let f e and f f denote the origination and termination points in the causal relationship, which are estimated as the first chronological observation whose test statistic respectively exceeds or falls below the critical value. The dating rules of the rolling and recursive evolving algorithms are given as:.

## Trading Bitcoin Futures with IBKR | IB Knowledge Base

For multiple switches, the origination and termination dates are calculated in a similar fashion. As Shi et al. Hence, we investigate the potential causal relationship using these two procedures in this paper. The minimum window size f 0 is set to 0. The critical values are obtained from a bootstrapping procedure with replications. Following Stock and Watson [] and Hasbrouck [] , Eq. This term is the major focus of different information share measures. In Hasbrouck [] , all the prices are equal in equilibrium because these series correspond to the prices of the same security being traded in multiple markets.

Thus, Eq. It can be decomposed as:. The first last represents the contribution to the common factor innovation from the first last market [ Baillie et al. When the covariance matrix is not diagonal, that is, the innovations are not independent, the IS of market j is given by Hasbrouck [] ,. This is known as the ordering problem where the calculation of IS using Eq.

Thus the IS measure of any market is not unique. Lien and Shrestha [] propose a new measure of information share to resolve the ordering problem of the Hasbrouck information share. The new measurement is called generalised modified information share GIS. GIS utilises a different factor structure that is based upon the correlation matrix of innovations instead of the covariance matrix. However, this assumption is restrictive since the one-to-one cointegrating relationship does not necessarily hold in the real world.

Therefore, such new measure can apply to series that do not have the one-to-one cointegrating relationships between them. When the innovations are independent, the variance of long-run impact on the i th series is:. The contribution of the innovation of series j to the total variance of the common factor of series i is then represented by:.

S j , i G is so called generalised information share GIS of series j which is independent of i. When the innovations are not independent, the GIS of series j can be calculated as:. It should be noted that the GIS measure uses the factor structure same as the MIS; thus it would also be independent of the ordering problem. We assume that error correction coefficients in Eq. Let S t and F t be the natural logarithms of daily prices of the spot and futures contacts, respectively.

If the two series are integrated at the same order, a potential cointegration relationship where the cointegrating coefficient is time variant rather than static, is represented as:.

## Cboe Abandons Bitcoin Futures

Therefore, Eq. Park and Hahn [] employ the superfluous regression approach to test the null hypothesis of the time-varying coefficient cointegration against the alternative of the spurious regression with non-stationary innovations. The corresponding test statistic is defined as:. In this paper, following the literature, we choose s to be 4.

In addition, we choose k from a range between 1 and 5. The optimal k is picked based on the adjusted R-square of CCR. The test statistic follows a Chi-square distribution with degree of freedom equal to the number of restrictions.

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- Bitcoin Futures on CBOE vs. CME: What's the Difference?.
- How Are Bitcoin Futures Similar to Other Types of Futures Contracts?.

It should be noted that the conditional variance-covariance matrix underlie the calculation of time-varying information share measures. Most of the applications of BGARCH models for estimating the optimal hedge ratio assume that the error terms follow a bivariate conditional normal distribution.

Typical distributional features of financial time-series data are excess kurtosis and asymmetry. In this paper, we employ a semi-nonparametric SNP approach to address the issue of excess kurtosis and non-zero skewness in the marginal return distribution. In particular, a two-step estimation procedure is applied to obtaining estimates for the individual GARCH processes, conditional correlation matrix and marginal skewness and kurtosis parameters.

First, the individual conditional variance equations are estimated via QMLE assuming Gaussian distribution and standardised innovations are obtained. Second, the parameters that capture the conditional correlation and other higher order moments are obtained via the log-likelihood maximization over the whole sample. The log-likelihood of the multivariate SNP density that each observation at time t contributes to, without unnecessary constant components, is shown as:. R t is conditional correlation matrix defined by Eq.

The procedure does not require pre-filtering the data but it require the maximum order of integration for the VAR. Using several unit root tests to check the stationarity of log futures and spot prices, we conclude that all variables are I 1.

### How Are Bitcoin Futures Different?

The time-varying Wald test statistics for causal effects from Bitcoin spot prices to CBOE futures prices along with their bootstrapped critical values are shown in Fig. The two rows illustrate the sequences of test statistics obtained from the rolling window and recursive evolving procedures respectively, while the columns of the figure refer to the two different assumptions for the residual error term homoskedasticity and heteroskedasticity for the VAR.

Sequences of the test statistics start from April Under different model and error assumptions presented in Fig. As a result, date-stamping results from Figs. The result suggests that the CBOE spot market may not be able to lead the futures market since the former responds to new information more slowly than the latter.

We can see that, first, there is little evidence of Granger causality episodes based on the rolling window procedure as presented in Fig. Second, the recursive evolving approach offers some different results. As shown in Fig. As a result, the null hypothesis of no Granger causality can be rejected. Similarly, under the error assumption of heteroscedasticity, Fig. As noted in Shi et al. Next, therefore, we undertake our analysis using the CME futures prices and CME BRR to explore the causal relationship between futures and spot markets with the results presented as in Fig.

For example, when we look at the date-stamping outcomes in Fig. When the recursive evolving procedure is applied as in Fig. Finally, we conduct an analysis of Granger causality running from the CME futures to spot prices. Interestingly, we obtain significant evidence to reject the null of no Granger causality from the CME futures to spot prices as presented in Fig.

The rolling window approach finds an episode of Granger causality between April and March in Fig. What is even more interesting is that the recursive evolving approach identifies an episode of Granger causality for the whole period between April and July as shown in Fig. It is clear that our results are robust to different error assumptions. As the recursive evolving approach has higher power over the rolling window approach, we prefer the results obtained from the recursive evolving approach.