Generalized Componentwise Splitting Scheme For Option Pricing Under The Heston-Cox-Ingersoll-Ross Model

Abstract

In this paper, we consider a numerical pricing of European call and put options under the Heston-Cox-Ingersoll-Ross (HCIR) model. Based on this model, the prices of options are derived by solving a three-dimensional partial differential equation. We generalize a componentwise splitting scheme for solving this equation. The idea of this scheme is to decompose the discretized HCIR partial differential equation into six one-dimensional equations in six fractional time steps. These equations are represented in tridiagonal systems, which are solved by the Thomas algorithm. Moreover, the numerical experiments show that the European option prices are affected by changes in volatility, interest rate, strike price, and correlation factors. Furthermore, numerical experiments compare the calculated prices based on our scheme with the prices reported in the literature.

Keywords

• Option pricing
• Stochastic volatility
• Stochastic interest rate
• Heston-Cox-Ingersoll-Ross model
• Componentwise splitting method