A Reduced Basis for Option Pricing

30 Pages Posted: 1 Oct 2010 Last revised: 20 Dec 2014

Rama Cont

Imperial College London; CNRS; Norges Bank Research

Nicolas Lantos

Olivier Pironneau

Université Paris VI Pierre et Marie Curie

Date Written: February 1, 2010

Abstract

We introduce a reduced basis method for the efficient numerical solution of partial integro-differential equations which arise in option pricing theory. Our method uses a basis of functions constructed from a sequence of Black-Scholes solutions with different volatilities. We show that this choice of basis leads to a sparse representation of option pricing functions, yielding an approximation whose precision is exponential in the number of basis functions. A Galerkin method using this basis for solving the pricing PDE is presented. Numerical tests based on the CEV diffusion model and the Merton jump diffusion model show that the method has better numerical performance relative to commonly used finite-difference and finite-element methods. We also compare our method with a numerical Proper Orthogonal Decomposition (POD). Finally, we show that this approach may be used advantageously for the calibration of local volatility functions.

Keywords: Option Pricing, PDE, Numerical Methods, PIDE, Jumps, Diffusion Models

JEL Classification: G13

Suggested Citation

Cont, Rama and Lantos, Nicolas and Pironneau, Olivier, A Reduced Basis for Option Pricing (February 1, 2010). Available at SSRN: https://ssrn.com/abstract=1685382 or http://dx.doi.org/10.2139/ssrn.1685382

Rama Cont (Contact Author)

Imperial College London ( email )

London, SW7 2AZ
United Kingdom

HOME PAGE: http://www3.imperial.ac.uk/people/r.cont

CNRS ( email )

Laboratoire de Probabilites & Modeles aleatoires
Universite Pierre & Marie Curie (Paris VI)
Paris, 75252
France

HOME PAGE: http://rama.cont.perso.math.cnrs.fr/

Norges Bank Research ( email )

P.O. Box 1179
Oslo, N-0107
Norway

Olivier Pironneau

Université Paris VI Pierre et Marie Curie ( email )

175 Rue du Chevaleret
Paris, 75013
France

No contact information is available for Nicolas Lantos

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