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

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journal contribution
posted on 2023-06-09, 03:50 authored by Bertram Duering, James Miles
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.

Funding

Novel discretisations for higher-order nonlinear PDE; Leverhulme; RPG-2015-69

DTA - University of Sussex 2013 (EPSRC); G1142; EPSRC-ENGINEERING & PHYSICAL SCIENCES RESEARCH COUNCIL; EP/L505109/1

History

Publication status

  • Published

File Version

  • Accepted version

Journal

Journal of Computational and Applied Mathematics

ISSN

0377-0427

Publisher

Elsevier

Volume

316

Page range

109-121

Department 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

2016-11-01

First Open Access (FOA) Date

2016-11-08

First Compliant Deposit (FCD) Date

2016-11-01

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