Estimating security price derivatives using simulation
Management Science
Forward start option pricing with stochastic volatility: a general framework
FEA '07 Proceedings of the Fourth IASTED International Conference on Financial Engineering and Applications
Sensitivity estimation of SABR model via derivative of random variables
Proceedings of the Winter Simulation Conference
Localization and Exact Simulation of Brownian Motion-Driven Stochastic Differential Equations
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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.