Bitcoin Futures and Option Markets: Searching for Completeness

Abstract

Cryptocurrencies have emerged in the last decade as a new asset class unlikely to disappear despite its extraordinary volatility. Futures contracts on Bitcoins were introduced in December 2017 by the Chicago Mercantile Exchange and options are being traded on crypto exchanges. Our goal in this paper is threefold: i) present the main features of cryptocurrency spot and derivative markets; ii) argue that storability of Bitcoins implies the existence of a convenience yield and infer from traded Future prices the risk neutral drift of the Bitcoin price in the continuous time Black-Scholes setting quite appropriate to continuously traded bitcoins. We use the prices of options traded on the Deribit Exchange to build the volatility smiles and skews observed at different dates of 2019 for short and long dated maturities and compare them to forward curves. Lastly, the robustness of the Black-Scholes formula allows capturing in our approach the stochastic volatility displayed by price trajectories and provides some answers to the incompleteness of the bitcoin market.

Keywords: Futures on Bitcoin, Convenience Yield for Bitcoin, Bitcoin smiles and skews, bitcoin market incompleteness