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Reduced Order Models (POD) for Calibration Problems in Finance

In: Numerical Mathematics and Advanced Applications

Author

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  • E. W. Sachs

    (Virginia Tech, Department of Mathematics
    Universität Trier, FB IV – Department of Mathematics)

  • M. Schu

    (Universität Trier, FB IV – Department of Mathematics)

Abstract

In this paper we consider the calibration of mathematical models for option pricing to observed data on the market. As a model for the underlying stock prices we use a jump diffusion process which results for the price of a call option in a partial integro-differential equation. We employ the dual - Dupire-type - version of it in order to improve the efficiency of the original calibration problem. To reduce the complexity of the problem even further, we use a reduced order model technique based on proper orthogonal decomposition techniques to obtain a model for the option price which is considerably smaller in size, but still copies the original model at a surprising accuracy. In the second half of the paper, we present numerical results which support these findings.

Suggested Citation

  • E. W. Sachs & M. Schu, 2008. "Reduced Order Models (POD) for Calibration Problems in Finance," Springer Books, in: Karl Kunisch & Günther Of & Olaf Steinbach (ed.), Numerical Mathematics and Advanced Applications, pages 735-742, Springer.
    • Handle: RePEc:spr:sprchp:978-3-540-69777-0_88
    DOI: 10.1007/978-3-540-69777-0_88
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