Reduced Order Models (POD) for Calibration Problems in Finance

E. W. Sachs () and M. Schu
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E. W. Sachs: Virginia Tech, Department of Mathematics
M. Schu: Universität Trier, FB IV – Department of Mathematics

A chapter in Numerical Mathematics and Advanced Applications, 2008, pp 735-742 from Springer

Abstract: 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.

Keywords: Option Price; Proper Orthogonal Decomposition; Call Option; Strike Price; Calibration Problem (search for similar items in EconPapers)
Date: 2008
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DOI: 10.1007/978-3-540-69777-0_88

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