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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 HeuerWe 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
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Publication status
- Published
File Version
- Accepted version
Publisher
Springer InternationalExternal DOI
Volume
25Page range
313-319Pages
626.0Book title
Novel Methods of Computational FinanceISBN
9783319612829Series
The European Consortium of Mathematics in IndustryDepartment 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 ErhhardtLegacy Posted Date
2017-09-04First Compliant Deposit (FCD) Date
2017-09-01Usage metrics
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