Pricing a Class of Exotic Options Via Moments and Sdp Relaxations

26 Pages Posted: 12 Jun 2006

See all articles by J.B. Lasserre

J.B. Lasserre

University of Angers - French National Center for Scientific Research (CNRS)

T. Prieto-Rumeau

National Distance Education University (UNED) - Faculty of Economics

Mihail Zervos

King's College London - Department of Mathematics

Abstract

We present a new methodology for the numerical pricing of a class of exotic derivatives such as Asian or barrier options when the underlying asset price dynamics are modeled by a geometric Brownian motion or a number of mean-reverting processes of interest. This methodology identifies derivative prices with infinite-dimensional linear programming problems involving the moments of appropriate measures, and then develops suitable finite-dimensional relaxations that take the form of semidefinite programs (SDP) indexed by the number of moments involved. By maximizing or minimizing appropriate criteria, monotone sequences of both upper and lower bounds are obtained. Numerical investigation shows that very good results are obtained with only a small number of moments. Theoretical convergence results are also established.

Suggested Citation

Lasserre, Jean Bernard and Prieto-Rumeau, Tomas and Zervos, Mihail, Pricing a Class of Exotic Options Via Moments and Sdp Relaxations. Mathematical Finance, Vol. 16, No. 3, pp. 469-494, July 2006, Available at SSRN: https://ssrn.com/abstract=907702 or http://dx.doi.org/10.1111/j.1467-9965.2006.00279.x

Jean Bernard Lasserre (Contact Author)

University of Angers - French National Center for Scientific Research (CNRS) ( email )

7 Avenue du Colonel Roche
31 077 Paris Cedex 13
France
+33 5 61 33 64 15 (Phone)
+33 5 61 33 69 36 (Fax)

HOME PAGE: http://www.laas.fr/~lasserre/

Tomas Prieto-Rumeau

National Distance Education University (UNED) - Faculty of Economics ( email )

Calle Senda del Rey, 11
28040 Madrid
Spain

HOME PAGE: http://www.seio.es/test/Archivos/t141/Test141prieto.pdf

Mihail Zervos

King's College London - Department of Mathematics ( email )

Strand
Strand
London, WC2R 2LS
United Kingdom

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