High-order compact finite difference scheme for option pricing in stochastic volatility jump models

Düring, Bertram and Pitkin, Alexander (2019) High-order compact finite difference scheme for option pricing in stochastic volatility jump models. Journal of Computational and Applied Mathematics, 355. pp. 201-217. ISSN 0377‐0427

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Abstract

We derive a new high-order compact finite difference scheme for option pricing in stochastic volatility jump models, e.g. in Bates model. In such models the option price is determined as the solution of a partial integro-differential equation. The scheme is fourth order accurate in space and second order accurate in time. Numerical experiments for the European option pricing problem are presented. We validate the stability of the scheme numerically and compare its performance to standard finite difference and finite element methods. The new scheme outperforms a standard discretisation based on a second-order central finite difference approximation in all our experiments. At the same time, it is very efficient, requiring only one initial -factorisation of a sparse matrix to perform the option price valuation. Compared to finite element approaches, it is very parsimonious in terms of memory requirements and computational effort, since it achieves high-order convergence without requiring additional unknowns, unlike finite element methods with higher polynomial order basis functions. The new high-order compact scheme can also be useful to upgrade existing implementations based on standard finite differences in a straightforward manner to obtain a highly efficient option pricing code.

Item Type: Article
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Research Centres and Groups: Numerical Analysis and Scientific Computing Research Group
Subjects: Q Science
Q Science > QA Mathematics
Depositing User: Alice Jackson
Date Deposited: 01 Feb 2019 12:09
Last Modified: 25 Feb 2019 16:00
URI: http://sro.sussex.ac.uk/id/eprint/81599

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Project NameSussex Project NumberFunderFunder Ref
Novel discretisations of higher-order nonlinear PDEG1603LEVERHULME TRUSTRPG-2015-069
EPSRC Doctoral Training PartnershipG1950EPSRC-ENGINEERING & PHYSICAL SCIENCES RESEARCH COUNCILEP/M506667/1