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Abstract
This paper aims to study the pricing of Bitcoin options with a view to incorporating both conditional heteroscedasticity and regime switching in Bitcoin returns. Specifically, a nonlinear time series model combining both the self-exciting threshold autoregressive (SETAR) model and the generalized autoregressive conditional heteroscedastic (GARCH) model is adopted for modeling Bitcoin return dynamics. Specifically, the SETAR model is used to model regime switching and the Heston-Nandi GARCH model is adopted to model conditional heteroscedasticity. Both the conditional Esscher transform and the variance-dependent pricing kernel are used to specify pricing kernels. Numerical studies on the Bitcoin option prices using real bitcoins data are presented.
Acknowledgments
We would like to thank the associate editor and the two referees for their helpful and insightful comments.
Disclosure statement
No potential conflict of interest was reported by the author(s).
Notes
1 We would like to thank the comments from a referee which inspired us to consider a variance-dependent pricing kernel in this paper.
2 The current Bitcoin price was taken as the close price of the CitationCoinDesk index on 31 May 2018; the current conditional variance was estimated by the sample variance of the daily logarithmic returns from the Coindesk index data; the daily logarithmic returns on the current day and the previous day were computed as the respective returns on 31 May 2018 and 30 May 2018 from the CoinDesk index data.
3 Siu (Citation2019a) conducted the statistical test of Hansen (Citation1999) to the daily percentage logarithmic returns from a Bitcoin exchange rate series in the U.S. dollar, namely ‘BitStamp’, and found evidence for the use of a two-regime SETAR model.