# Change of measure in a Heston-Hawkes stochastic volatility model

ADVANCES IN APPLIED PROBABILITY（2024）

Abstract

We consider the stochastic volatility model obtained by adding a compound Hawkes process to the volatility of the well-known Heston model. A Hawkes process is a self-exciting counting process with many applications in mathematical finance, insurance, epidemiology, seismology, and other fields. We prove a general result on the existence of a family of equivalent (local) martingale measures. We apply this result to a particular example where the sizes of the jumps are exponentially distributed. Finally, a practical application to efficient computation of exposures is discussed.

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Key words

Stochastic volatility,change of measure,risk-neutral measure,existence of equivalent martingale measure,non-Markovian model,Hawkes process,volatility with jumps

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