Time-Adaptive High-Order Compact Finite Difference Schemes for Option Pricing in a Family of Stochastic Volatility Models

Abstract

AbstractWe propose a time-adaptive high-order compact finite difference scheme for option pricing in a family of stochastic volatility models. We employ a semi-discrete high-order compact finite difference method for the spatial discretisation, and combine this with an adaptive time discretisation, extending ideas from Lötstedt et al. (Implicit solution of hyperbolic equations with space-time adaptivity, BIT, 42(1):134–158, 2002.) to fourth-order multistep methods in time.