AN EFFICIENT OPERATOR SPLITTING TECHNIQUE FOR OPTION PRICING UNDER STOCHASTIC VOLATILITY

Abstract

Stochastic Volatility models are more realistic than the Black-Scholes model for Vanilla option pricing, because risk neutrality assumption is avoided. We solve He ston’s stochastic volatility model, that has been solved using Monte-Carlo method which is computationally realistic in the third dimension only; and Finite difference methods that are more efficient, but face curse of dimensionality in at least three dimensions. This study adopts the Strang’s operator splitting method that uses stochastically weighted sub-problems. Fourth order Runge-Kutta method for partial differential equations are used within finite difference formulations of the split sub-problems. Charpit method is applied in the nonlinear part of the Option pricing model. The method has second order truncation error and is computationally more realistic, which is verified by the Chicago Board of Options Exchange data. The running time of computer powered simulations are lower than those found in the two methods.