Pricing Cryptocurrency Options

TL;DR

This paper introduces a stochastic volatility with correlated jump model for pricing Bitcoin options, highlighting the significant impact of jumps and co-jumps on option prices and implied volatility, marking pioneering research in cryptocurrency option pricing.

Contribution

It proposes a novel SVCJ model for cryptocurrency options and compares it with existing co-jump models, emphasizing the role of jumps in market dynamics.

Findings

Jumps and co-jumps significantly influence option prices.

A sizeable proportion of price jumps are anti-correlated with volatility jumps.

The model effectively captures the impact of jumps on implied volatility.

Abstract

Cryptocurrencies, especially Bitcoin (BTC), which comprise a new digital asset class, have drawn extraordinary worldwide attention. The characteristics of the cryptocurrency/BTC include a high level of speculation, extreme volatility and price discontinuity. We propose a pricing mechanism based on a stochastic volatility with a correlated jump (SVCJ) model and compare it to a flexible co-jump model by Bandi and Ren\`o (2016). The estimation 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 the proposed pricing mechanism underlines the importance of jumps in cryptocurrency markets.