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High-order compact finite difference scheme for option pricing in stochastic volatility jump models
journal contribution
posted on 2023-06-09, 16:43 authored by Bertram Duering, Alexander PitkinWe 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.
Funding
EPSRC Doctoral Training Partnership; G1950; EPSRC-ENGINEERING & PHYSICAL SCIENCES RESEARCH COUNCIL; EP/M506667/1
Novel discretisations of higher-order nonlinear PDE; G1603; LEVERHULME TRUST; RPG-2015-069
History
Publication status
- Published
File Version
- Accepted version
Journal
Journal of Computational and Applied MathematicsISSN
0377-0427Publisher
ElsevierExternal DOI
Volume
355Page range
201-217Department affiliated with
- Mathematics Publications
Research groups affiliated with
- Numerical Analysis and Scientific Computing Research Group Publications
Full text available
- Yes
Peer reviewed?
- Yes
Legacy Posted Date
2019-02-01First Open Access (FOA) Date
2020-02-07First Compliant Deposit (FCD) Date
2019-01-31Usage metrics
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