[Comportement asymptotique de la distribution du prix de l'action dans les modèles à volatilité stochastique : le modèle de Hull–White]
La présente Note étudie le comportement asymptotique de la densité de distribution du processus du prix de l'action dans le modèle de Hull–White. On determine la partie principale dans le développement asymptotique en zéro et en l'infini pour une telle densité et on estime l'erreur correspondante. Des problèmes similaires se résolvent pour les moyennes temporelles du processus de volatilité qui sont aussi intéressants dans l'étude des options asiatiques.
In the present Note, we study the asymptotic behavior of the distribution density of the stock price process in the Hull–White model. The leading terms in the asymptotic expansions at zero and infinity are found for such a density and the corresponding error estimates are given. Similar problems are solved for time averages of the volatility process, which are also of interest in the study of Asian options.
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@article{CRMATH_2006__343_8_519_0,
author = {Gulisashvili, Archil and Stein, Elias M.},
title = {Asymptotic behavior of the distribution of the stock price in models with stochastic volatility: the {Hull{\textendash}White} model},
journal = {Comptes Rendus. Math\'ematique},
pages = {519--523},
publisher = {Elsevier},
volume = {343},
number = {8},
year = {2006},
doi = {10.1016/j.crma.2006.09.029},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2006.09.029/}
}
TY - JOUR AU - Gulisashvili, Archil AU - Stein, Elias M. TI - Asymptotic behavior of the distribution of the stock price in models with stochastic volatility: the Hull–White model JO - Comptes Rendus. Mathématique PY - 2006 SP - 519 EP - 523 VL - 343 IS - 8 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2006.09.029/ DO - 10.1016/j.crma.2006.09.029 LA - en ID - CRMATH_2006__343_8_519_0 ER -
%0 Journal Article %A Gulisashvili, Archil %A Stein, Elias M. %T Asymptotic behavior of the distribution of the stock price in models with stochastic volatility: the Hull–White model %J Comptes Rendus. Mathématique %D 2006 %P 519-523 %V 343 %N 8 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2006.09.029/ %R 10.1016/j.crma.2006.09.029 %G en %F CRMATH_2006__343_8_519_0
Gulisashvili, Archil; Stein, Elias M. Asymptotic behavior of the distribution of the stock price in models with stochastic volatility: the Hull–White model. Comptes Rendus. Mathématique, Tome 343 (2006) no. 8, pp. 519-523. doi : 10.1016/j.crma.2006.09.029. http://www.numdam.org/articles/10.1016/j.crma.2006.09.029/
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