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A priori error estimates for reduced ordermodels in finance∗

Published online by Cambridge University Press:  11 January 2013

Ekkehard W. Sachs  and
Matthias Schu
Ekkehard W. Sachs
Affiliation:
Universität Trier, Fachbereich IV, Abteilung Mathematik, 54286 Trier, Germany.. sachs@uni-trier.de; schu@uni-trier.de
Matthias Schu
Affiliation:
Universität Trier, Fachbereich IV, Abteilung Mathematik, 54286 Trier, Germany.. sachs@uni-trier.de; schu@uni-trier.de
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Abstract

Mathematical models for option pricing often result in partial differential equations.Recent enhancements are models driven by Lévy processes, which lead to a partialdifferential equation with an additional integral term. In the context of modelcalibration, these partial integro differential equations need to be solved quitefrequently. To reduce the computational cost the implementation of a reduced order modelhas shown to be very successful numerically. In this paper we give a priorierror estimates for the use of the proper orthogonal decomposition technique inthe context of option pricing models.

Keywords

Option pricing modelsproper orthogonal decompositiona priori error estimate

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Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 47 , Issue 2 , March 2013 , pp. 449 - 469
Copyright
© EDP Sciences, SMAI, 2013

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