Comptes Rendus
no. 8
Probability Theory
Asymptotic behavior of the distribution of the stock price in models with stochastic volatility: the Hull–White model
[Comportement asymptotique de la distribution du prix de l'action dans les modèles à volatilité stochastique : le modèle de Hull–White]

Présenté par : Jean-Pierre Kahane

Archil Gulisashvili1 ; Elias M. Stein2
1 Department of Mathematics, Ohio University, Athens, OH 45701, USA
2 Department of Mathematics, Princeton University, Princeton, NJ 08540, USA
Comptes Rendus. Mathématique, Volume 343 (2006) no. 8, pp. 519-523.

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.

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.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2006.09.029

Archil Gulisashvili 1 ; Elias M. Stein 2

1 Department of Mathematics, Ohio University, Athens, OH 45701, USA
2 Department of Mathematics, Princeton University, Princeton, NJ 08540, USA 
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Archil Gulisashvili; Elias M. Stein. Asymptotic behavior of the distribution of the stock price in models with stochastic volatility: the Hull–White model. Comptes Rendus. Mathématique, Volume 343 (2006) no. 8, pp. 519-523. doi : 10.1016/j.crma.2006.09.029. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2006.09.029/

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