Exact Simulation of Option Greeks under Stochastic Volatility and Jump Diffusion Models

Abstract

This paper derives Monte Carlo simulation estimators to compute option price derivatives, i.e., the 'Greeks,' under Heston's stochastic volatility model and some variants of it which include jumps in the price and variance processes. We use pathwise and likelihood ratio approaches together with the exact simulation method of Broadie and Kaya (2004) to generate unbiased estimates of option price derivatives in these models. By appropriately conditioning on the path generated by the variance and jump processes, the evolution of the stock price can be represented as a series of lognormal random variables. This makes it possible to extend previously known results from the Black-Scholes setting to the computation of Greeks for more complex models. We give simulation estimators and numerical results for some path-dependent and path-independent options.