USING EXOTIC OPTION PRICES AS CONTROL VARIATES IN MONTE CARLO PRICING UNDER A LOCAL-STOCHASTIC VOLATILITY MODEL

Abstract

A Monte Carlo numerical method is developed for using a hybrid localstochastic volatility (LSV) model to price exotic options, in particular barrier options. We use market traded data on AUD/USD and AUD/JPY to benchmark the accuracy of the implemented method for pricing barrier options traded in the global foreign-exchange options market. We show that the implemented LSV model can accurately reproduce market implied volatilities for vanilla options. A PDE pricing engine for the LSV model has been used as the benchmark method to examine the performance of the Monte Carlo engine for which two different control variates are incorporated to reduce pricing variances in the Monte Carlo results. The numerical results shown in this paper suggest that the best improvement in accuracy is obtained when utilising market-traded exotic options as control variates to price other exotic options, whereas using vanilla options as conventional control variates is not as effective, because the exotic option control variate can provide additional market information to correct the LSV model error.