[Loi de la fonctionnelle exponentielle de processus de Lévy assymétriques et options asiatiques]
L'object de cette Note est de donner une représentation, en terme d'une série entière, de la distribution de la fonctionnelle exponentielle, considérée en un temps exponentiel indépendant, d'un processus de Lévy ξ spectralement négatif, à variation infinie et pouvant être tué. Nous en déduisons une formule du type Geman–Yor pour le prix des options asiatiques dans un marché financier dirigé par .
The purpose of this Note is to describe, in terms of a power series, the distribution function of the exponential functional, taken at some independent exponential time, of a spectrally negative Lévy process with unbounded variation. We also derive a Geman–Yor type formula for Asian options prices in a financial market driven by .
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@article{CRMATH_2009__347_7-8_407_0,
author = {Patie, Pierre},
title = {Law of the exponential functional of one-sided {L\'evy} processes and {Asian} options},
journal = {Comptes Rendus. Math\'ematique},
pages = {407--411},
publisher = {Elsevier},
volume = {347},
number = {7-8},
year = {2009},
doi = {10.1016/j.crma.2009.02.013},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2009.02.013/}
}
TY - JOUR AU - Patie, Pierre TI - Law of the exponential functional of one-sided Lévy processes and Asian options JO - Comptes Rendus. Mathématique PY - 2009 SP - 407 EP - 411 VL - 347 IS - 7-8 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2009.02.013/ DO - 10.1016/j.crma.2009.02.013 LA - en ID - CRMATH_2009__347_7-8_407_0 ER -
%0 Journal Article %A Patie, Pierre %T Law of the exponential functional of one-sided Lévy processes and Asian options %J Comptes Rendus. Mathématique %D 2009 %P 407-411 %V 347 %N 7-8 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2009.02.013/ %R 10.1016/j.crma.2009.02.013 %G en %F CRMATH_2009__347_7-8_407_0
Patie, Pierre. Law of the exponential functional of one-sided Lévy processes and Asian options. Comptes Rendus. Mathématique, Tome 347 (2009) no. 7-8, pp. 407-411. doi : 10.1016/j.crma.2009.02.013. http://www.numdam.org/articles/10.1016/j.crma.2009.02.013/
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