High-order ADI scheme for option pricing in stochastic volatility models

TL;DR

This paper introduces a high-order ADI finite difference scheme that achieves fourth-order spatial and second-order temporal accuracy for option pricing models with stochastic volatility, improving computational efficiency and precision.

Contribution

It develops a novel high-order ADI scheme combining advanced spatial discretizations with ADI time-stepping for stochastic volatility models in option pricing.

Findings

The scheme is fourth-order accurate in space.

The scheme is second-order accurate in time.

Numerical experiments confirm high-order convergence.

Abstract

We propose a new high-order alternating direction implicit (ADI) finite difference scheme for the solution of initial-boundary value problems of convection-diffusion type with mixed derivatives and non-constant coefficients, as they arise from stochastic volatility models in option pricing. Our approach combines different high-order spatial discretisations with Hundsdorfer and Verwer's ADI time-stepping method, to obtain an efficient method which is fourth-order accurate in space and second-order accurate in time. Numerical experiments for the European put option pricing problem using Heston's stochastic volatility model confirm the high-order convergence.