High-Order Compact Finite Difference Scheme for Option Pricing in Stochastic Volatility With Contemporaneous Jump Models

Abstract

We extend the scheme developed in B. During, A. We extend the scheme developed in B. During, A. Pitkin, "High-order compact finite difference scheme for option pricing in stochastic volatility jump models", 2019, to the so-called stochastic volatility with contemporaneous jumps (SVCJ) model, derived by Duffie, Pan and Singleton. The performance of the scheme is assessed through a number of numerical experiments, using comparisons against a standard second-order central difference scheme. We observe that the new high-order compact scheme achieves fourth order convergence and discuss the effects on efficiency and computation time.