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

Düring, Bertram and Miles, James (2016) High-order ADI scheme for option pricing in stochastic volatility models. Journal of Computational and Applied Mathematics, 316. pp. 109-121. ISSN 0377-0427

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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.

Item Type: Article
Keywords: Option pricing; Stochastic volatility models; Mixed derivatives; High-order ADI scheme
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Research Centres and Groups: Numerical Analysis and Scientific Computing Research Group
Subjects: Q Science > QA Mathematics
Depositing User: Richard Chambers
Date Deposited: 01 Nov 2016 13:45
Last Modified: 20 Aug 2017 16:32
URI: http://sro.sussex.ac.uk/id/eprint/65209

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Project NameSussex Project NumberFunderFunder Ref
Novel discretisations for higher-order nonlinear PDEUnsetLeverhulmeRPG-2015-69
DTA - University of Sussex 2013 (EPSRC)G1142EPSRC-ENGINEERING & PHYSICAL SCIENCES RESEARCH COUNCILEP/L505109/1