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Novel Methods in Computational Finance pp 295–312Cite as

Sparse Grid High-Order ADI Scheme for Option Pricing in Stochastic Volatility Models

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Part of the book series: Mathematics in Industry ((TECMI,volume 25))

Abstract

We present a sparse grid high-order alternating direction implicit (ADI) scheme for option pricing in stochastic volatility models. The scheme is second-order in time and fourth-order in space. Numerical experiments confirm the computational efficiency gains achieved by the sparse grid combination technique.

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Acknowledgements

BD acknowledges support by the Leverhulme Trust research project grant ‘Novel discretisations for higher-order nonlinear PDE’ (RPG-2015-69). CH is supported by the European Union in the FP7-PEOPLE-2012-ITN Program under Grant Agreement Number 304617 (FP7 Marie Curie Action, Project Multi-ITN STRIKE—Novel Methods in Computational Finance). Further CH acknowledges partial support from the bilateral German-Spanish Project HiPeCa—High Performance Calibration and Computation in Finance, Programme Acciones Conjuntas Hispano-Alemanas financed by DAAD. JM has been supported in part by a studentship under the EPSRC Doctoral Training Partnership (DTP) scheme (grant number EP/L505109/1).

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Authors and Affiliations

  1. Department of Mathematics, University of Sussex, Pevensey II, BN1 9QH, Brighton, UK

    Bertram Düring & James Miles

  2. Chair of Applied Mathematics/Numerical Analysis, Bergische Universität Wuppertal, Gaußstraße 20, 42097, Wuppertal, Germany

    Christian Hendricks

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  1. Bertram Düring
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  2. Christian Hendricks
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  3. James Miles
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Correspondence to Bertram Düring .

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Editors and Affiliations

  1. Lehrstuhl für Angewandte Mathematik/Numerische Analysis, Bergische Universität Wuppertal, Wuppertal, Germany

    Matthias Ehrhardt

  2. Lehrstuhl für Angewandte Mathematik/Numerische Analysis, Bergische Universität Wuppertal, Wuppertal, Germany

    Michael Günther

  3. Lehrstuhl für Angewandte Mathematik/Numerische Analysis, Bergische Universität Wuppertal, Wuppertal, Germany

    E. Jan W. ter Maten

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Düring, B., Hendricks, C., Miles, J. (2017). Sparse Grid High-Order ADI Scheme for Option Pricing in Stochastic Volatility Models. In: Ehrhardt, M., Günther, M., ter Maten, E. (eds) Novel Methods in Computational Finance. Mathematics in Industry(), vol 25. Springer, Cham. https://doi.org/10.1007/978-3-319-61282-9_16

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