An Efficient Operator Splitting Technique for Option Pricing under Stochastic Volatility

By: Patrick Chidzalo, Charles Fodya,

Abstract

Stochastic Volatility models are more realistic than the Black-Scholes model for Vanilla option pricing because the risk neutrality assumption is eliminated. We solve Heston’s stochastic volatility model using Strang’s operator splitting method that uses weighted sub-problems. Fourth order Runge-Kutta method for partial differential equations are used within finite difference formulations of the split sub-problems. Charpit-Lagrange method is applied in the non-linear part of the model. The method has second order truncation error and it is also computationally more realistic, which is verified with Chicago Board of Options Exchange data. The running times for computer powered simulation are lower than those found in the two methods.