PRICING A CLASS OF EXOTIC OPTIONS VIA MOMENTS AND SDP RELAXATIONS

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 pri...

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Vydáno v:Mathematical finance Ročník 16; číslo 3; s. 469 - 494
Hlavní autoři: Lasserre, J. B., Prieto-Rumeau, T., Zervos, M.
Médium: Journal Article
Jazyk:angličtina
Vydáno: Malden, USA Blackwell Publishing Inc 01.07.2006
Wiley Blackwell
Blackwell Publishing Ltd
Edice:Mathematical Finance
Témata:
Appropriateness
Asset valuation
Brownian motion
Convergence
Derivatives
exotic options
Financial economics
Linear programming
Mathematical economics
Mathematical models
moments of measures
Option pricing
options pricing
Options trading
Prices
semidefinite programming
Sequences
Statistical models
Stochastic models
Studies
Asia
Europe
ISSN:0960-1627, 1467-9965
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Popis
Shrnutí: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.
Bibliografie:istex:2903D4EDFECF066911DB96E162EDFFD61A6D2578
ark:/67375/WNG-G0V30XD2-L
ArticleID:MAFI279
We would like to thank Jordan Stoyanov for a number of most useful and inspiring discussions on the results presented in this paper. We are also grateful to the anonymous referees whose comments lead to a significant improvement of our original manuscript. The research of the first and third authors was part of project no. 03996QF within the France–Great Britain Alliance program for research cooperation. The second author was supported by a grant from the Spanish
Secretaría de Estado de Educación y Universidades
in cooperation with the European Social Funds.
Manuscript received September 2003; final revision received April 2005.
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ISSN:0960-1627
1467-9965
DOI:10.1111/j.1467-9965.2006.00279.x