A combined compact difference scheme for option pricing in the exponential jump-diffusion models

• Main Authors: Rahman Akbari, Reza Mokhtari, Mohammad Taghi Jahandideh
• Format: Article
• Language: English
• Published: SpringerOpen 2019-12-01
• Series: Advances in Difference Equations
• Subjects: Black–Scholes equation; Combined compact difference (CCD); Jump-diffusion model; Option pricing
• Online Access: https://doi.org/10.1186/s13662-019-2431-7

Abstract In the present paper, starting with the Black–Scholes equations, whose solutions are the values of European options, we describe the exponential jump-diffusion model of Levy process type. Here, a jump-diffusion model for a single-asset market is considered. Under this assumption the value of a European contingency claim satisfies a general “partial integro-differential equation” (PIDE). With a combined compact difference (CCD) scheme for the spatial discretization, a high-order method is proposed for solving exponential jump-diffusion models. The method is sixth-order accurate in space and second-order accurate in time. A known analytical solution to the model is used to evaluate the performance of the numerical scheme.