An asymptotic expansion for a Black-Scholes type model

被引：3
|
作者：
Lütkebohmert, E [1 ]
机构：
[1] Univ Bonn, Inst Angew Math, Abt Stockast, D-53115 Bonn, Germany
来源：
BULLETIN DES SCIENCES MATHEMATIQUES | 2004年 / 128卷 / 08期
关键词：
Black-Scholes model; asymptotic expansion; Malliavin calculus; borel summability; small diffusion; Laplace method;
D O I：
10.1016/j.bulsci.2004.02.008
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We consider the Black-Scholes model where we add a perturbation term Sigma(i) epsilon(i)sigma(i) to the model with diffusion coefficient sigma(0)(t). Then we derive an asymptotic expansion for the expected value of an European call option at time t. This is done by applying methods of Malliavin calculus. Borel summability of the derived asymptotic expansion is proven. (C) 2004 Elsevier SAS. All rights reserved.
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页码：661 / 685
页数：25
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