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A study of the Hartman–Watson distribution motivated by numerical problems related to the pricing of Asian options

Part of: Distribution theory Distribution theory - Probability Probabilistic methods, simulation and stochastic differential equations Markov processes

Published online by Cambridge University Press:  14 July 2016

P. Barrieu ,
A. Rouault  and
M. Yor
P. Barrieu*
Affiliation:
London School of Economics
A. Rouault*
Affiliation:
University of Versailles
M. Yor*
Affiliation:
University of Paris VI
*
∗ Postal address: Department of Statistics, London School of Economics, Houghton Street, London WC2A 2AE, UK. Email address: p.m.barrieu@lse.ac.uk
∗∗ Postal address: Department of Mathematics, University of Versailles, 45 avenue des Etats-Unis, 78035 Versailles cedex, France
∗∗∗ Postal address: Laboratoire de Probabilités et Modèles Aléatoires, University of Paris VI, 175 rue du Chevaleret, 75013 Paris, France
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Abstract

One approach to the computation of the price of an Asian option involves the Hartman–Watson distribution. However, numerical problems for its density occur for small values. This motivates the asymptotic study of its distribution function.

Keywords

Asian optionHartman–Watson distributionlarge deviation

MSC classification

Primary: 60J65: Brownian motion 60E99: None of the above, but in this section
Secondary: 62E20: Asymptotic distribution theory 65C50: Other computational problems in probability
Type
Research Papers
Information
Journal of Applied Probability , Volume 41 , Issue 4 , December 2004 , pp. 1049 - 1058
Copyright
Copyright © Applied Probability Trust 2004 

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