Pricing Cryptocurrency Options: The Case of Bitcoin and CRIX

Abstract

Cryptocurrencies, especially Bitcoin (BTC), which comprise a new revolutionary asset class, have drawn extraordinary worldwide attention. The characteristics of the cryptocurrency/ BTC include a high level of speculation, extreme volatility and price discontinuity. In this paper, we propose a pricing mechanism based on a stochastic volatility with correlated jump (SVCJ) model and compare it to a flexible co-jump model by Bandi and Renò (2016) allowing for non-affine structure. The calibration results of both models confirm the impact of jumps and co-jumps on options obtained via simulation and an analysis of the implied volatility curve. We show that a sizeable proportion of price jumps are significantly and contemporaneously anti-correlated with jumps in volatility. Our study comprises pioneering research on pricing BTC options. We show how proposed pricing mechanism underscores the importance of jumps in the cryptocurrency derivatives markets.

Keywords: Cryptocurrency IndeX, CRIX, Bitcoin, Cryptocurrency, SVCJ, Option pricing, OCRIX

JEL Classification: C32, C58, C52