High-Order ADI Scheme for Option Pricing in Stochastic Volatility Models
18 Pages Posted: 9 Dec 2015
Date Written: December 8, 2015
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.
Keywords: Option pricing, stochastic volatility models, mixed derivatives, high-order ADI scheme
JEL Classification: C63, G13
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