Jump risk premia in the presence of clustered jumps

This paper presents an option pricing model that incorporates clustered jumps using a bivariate Hawkes process. The process captures both self- and cross-excitation of positive and negative jumps, enabling the model to generate return dynamics with asymmetric, time-varying skewness and to produce positive or negative implied volatility skews. This feature is especially relevant for assets such as cryptocurrencies, so-called ``meme'' stocks, G-7 currencies, and certain commodities, where implied volatility skews may change sign depending on prevailing sentiment. We introduce two additional parameters, namely the positive and negative jump premia, to model the market risk preferences for positive and negative jumps, inferred from options data. This enables the model to flexibly match observed skew dynamics. Using Bitcoin (BTC) options, we empirically demonstrate how inferred jump risk premia exhibit predictive power for both the cost of carry in BTC futures and the performance of delta-hedged option strategies.