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Pricing of Basket Options Using Dimension Reduction and Adaptive Finite Differences in Space, and Discontinuous Galerkin in Time

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Numerical Mathematics and Advanced Applications ENUMATH 2015

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 112))

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Abstract

European basket options are priced by solving the multi-dimensional Black–Scholes–Merton equation. Standard numerical methods to solve these problems often suffer from the “curse of dimensionality”. We tackle this by using a dimension reduction technique based on a principal component analysis with an asymptotic expansion. Adaptive finite differences are used for the spatial discretization. In time we employ a discontinuous Galerkin scheme. The efficiency of our proposed method to solve a five-dimensional problem is demonstrated through numerical experiments and compared with a Monte-Carlo method.

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Author information

Authors and Affiliations

  1. Department of Information Technology, Uppsala University, Uppsala, Sweden

    Lina von Sydow, Paria Ghafari, Erik Lehto & Mats Wångersjö

  2. Department of Mathematics, KTH Royal Institute of Technology, Stockholm, Sweden

    Erik Lehto

Authors
  1. Lina von Sydow
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  2. Paria Ghafari
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  3. Erik Lehto
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  4. Mats Wångersjö
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Corresponding author

Correspondence to Lina von Sydow .

Editor information

Editors and Affiliations

  1. Mathematics & Applied Mathematics, Middle East Technical University Mathematics & Applied Mathematics, Ankara, Turkey

    Bülent Karasözen

  2. Dept of Computer Engg, Middle East Technical Univ Dept of Computer Engg, Cankaya, Ankara, Turkey

    Murat Manguoğlu

  3. Middle East Technical University Mathematics & Institute of Applied Mathe, Ankara, Turkey

    Münevver Tezer-Sezgin

  4. Civil Engineering & Applied Mathematics, Middle East Technical University, Ankara, Turkey

    Serdar Göktepe

  5. Institute of Applied Mathematics, Middle East Technical University Institute of Applied Mathematics, Ankara, Turkey

    Ömür Uğur

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von Sydow, L., Ghafari, P., Lehto, E., Wångersjö, M. (2016). Pricing of Basket Options Using Dimension Reduction and Adaptive Finite Differences in Space, and Discontinuous Galerkin in Time. In: Karasözen, B., Manguoğlu, M., Tezer-Sezgin, M., Göktepe, S., Uğur, Ö. (eds) Numerical Mathematics and Advanced Applications ENUMATH 2015. Lecture Notes in Computational Science and Engineering, vol 112. Springer, Cham. https://doi.org/10.1007/978-3-319-39929-4_58

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