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Essentially high-order compact schemes with application to stochastic volatility models on non-uniform grids

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posted on 2023-06-09, 07:46 authored by Bertram Duering, Christof Heuer
We present high-order compact schemes for a linear second-order parabolic partial differential equation (PDE) with mixed second-order derivative terms in two spatial dimensions. The schemes are applied to option pricing PDE for a family of stochastic volatility models. We use a non- uniform grid with more grid-points around the strike price. The schemes are fourth-order accurate in space and second-order accurate in time for vanishing correlation. In our numerical convergence study we achieve fourth-order accuracy also for non-zero correlation. A combination of Crank-Nicolson and BDF-4 discretisation is applied in time. Numerical examples confirm that a standard, second-order infinite difference scheme is significantly outperformed.

Funding

Novel discretisations of higher-order nonlinear PDE; G1603; LEVERHULME TRUST; RPG-2015-069

History

Publication status

  • Published

File Version

  • Accepted version

Publisher

Springer International

Volume

25

Page range

313-319

Pages

626.0

Book title

Novel Methods of Computational Finance

ISBN

9783319612829

Series

The European Consortium of Mathematics in Industry

Department affiliated with

  • Mathematics Publications

Research groups affiliated with

  • Numerical Analysis and Scientific Computing Research Group Publications

Full text available

  • No

Peer reviewed?

  • Yes

Editors

E. Jan W ter Maten, Michael Gunther, Matthias Erhhardt

Legacy Posted Date

2017-09-04

First Compliant Deposit (FCD) Date

2017-09-01

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