Model Reduction Methods in Option Pricing

Francisco Chinesta (), Antonio Falcó and Mariano Gonzalez Sanchez
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Francisco Chinesta: LMSP - Laboratoire de Mécanique des Systèmes et des Procédés - CNRS - Centre National de la Recherche Scientifique

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Abstract: In this work we introduce the Proper Orthogonal Decomposition (POD) approach to the valuation of contingent claims for one–dimensional price models. First, we present the POD in the context of an abstract Hilbert space and we give an application for the numerical pricing of Double Barrier Options. In a finite dimension setting, we show the model reduction method for Finite Difference schemes of implicit type. In particular, we construct the reduced version of the Crank–Nicolson scheme and some numerical examples are given.

Keywords: Model Reduction; Proper Orthogonal Decomposition; Finite Difference Schemes; Crank-Nicolson Scheme (search for similar items in EconPapers)
Date: 2006
Note: View the original document on HAL open archive server: https://hal.science/hal-00289700
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Published in Journal electronique de l'Instituto Valenciano de Investigaciones Economicas, 2006

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Working Paper: MODEL REDUCTION METHODS IN OPTION PRICING (2006)
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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-00289700

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