2025/10/24 by Francis Liu, Liu, Francis, Natalie Packham +3 · 2 voices
Biochemistry, Genetics and Molecular Biology · Economics, Econometrics and Finance · Mathematics · #60G55 #91G20 #Diffusion and Search Dynamics #FOS: Economics and business #Mathematical Finance (q-fin.MF) #Point processes and geometric inequalities #Pricing of Securities (q-fin.PR) #Stochastic processes and financial applications #q-fin.MF #q-fin.PR
paper · pdf · doi:10.48550/arxiv.2510.21297
openalex publication_date 2025/10/24 · arxiv published 2025/10/24 · arxiv updated 2025/10/24 · openalex created_date 2025/10/28 · openalex updated_date 2026/07/28
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.