Dűring, Bertram and Heuer, Christof (2017) Essentially high-order compact schemes with application to stochastic volatility models on non-uniform grids. In: Erhhardt, Matthias, Gunther, Michael and ter Maten, E. Jan W (eds.) Novel Methods of Computational Finance. The European Consortium of Mathematics in Industry, 25 . Springer International, pp. 313-319. ISBN 9783319612829
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Abstract
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.
Item Type: | Book Section |
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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 |
Related URLs: | |
Depositing User: | Billy Wichaidit |
Date Deposited: | 04 Sep 2017 08:08 |
Last Modified: | 19 Oct 2017 11:17 |
URI: | http://srodev.sussex.ac.uk/id/eprint/69974 |
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📧 Request an updateProject Name | Sussex Project Number | Funder | Funder Ref |
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Novel discretisations of higher-order nonlinear PDE | G1603 | LEVERHULME TRUST | RPG-2015-069 |