The Fourier-series method for inverting transforms of probability distributions
Queueing Systems: Theory and Applications - Numerical computations in queues
Exact simulation of option greeks under stochastic volatility and jump diffusion models
WSC '04 Proceedings of the 36th conference on Winter simulation
Sensitivity Estimates from Characteristic Functions
Operations Research
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We derive Monte Carlo simulation estimators to compute option price sensitivities under the SABR stochastic volatility model. As a companion to the exact simulation method developed by Cai, Chen and Song (2011), this paper uses the sensitivity of "vol of vol" as a showcase to demonstrate how to use the pathwise method to obtain unbiased estimators to the price sensitivities under SABR. By appropriately conditioning on the path generated by the volatility, the evolution of the forward price can be represented as noncentral chi-square random variables with stochastic parameters. Combined with the technique of derivative of random variables, we can obtain fast and accurate unbiased estimators for the sensitivities.