Description

This paper presents a novel option pricing model that incorporates clusters of jumps using a bivariate Hawkes process with exponential decay memory kernels. The Hawkes process characterises the self- and cross-excitement of positive jumps and negative jumps, allowing the model to effectively capture the volatile Bitcoin (BTC) price dynamics, especially the jump arrival times, and the BTC implied volatility smiles. We explore the positive and negative jump risk premia, defined as the discrepancies in jump measures between the objective measure and the risk-neutral measure.

Our findings reveal that these jump risk premia: (i) provide insights on how the BTC options market reacted to major events, such as the COVID-19 outbreak and the FTX scandal; (ii) posses significant predictive power for delta-hedged option returns; and (iii) are indicators in explaining the volatile cost-of-carry implied from BTC futures prices.