Short-Maturity Asymptotics for a Fast Mean-Reverting Heston Stochastic Volatility Model

被引：37
|
作者：
Feng, Jin [1 ]
Forde, Martin [2 ]
Fouque, Jean-Pierre [3 ]
机构：
[1] Univ Kansas, Dept Math, Lawrence, KS 66045 USA
[2] Dublin City Univ, Dept Math Sci, Dublin 9, Ireland
[3] Univ Calif Santa Barbara, Dept Stat & Appl Probabil, Santa Barbara, CA 93016 USA
来源：
SIAM JOURNAL ON FINANCIAL MATHEMATICS | 2010年 / 1卷 / 01期
基金：
美国国家科学基金会;
关键词：
stochastic volatility; Heston model; multiscale asymptotics; large deviation principle; implied volatility smile/skew; IMPLIED VOLATILITY;
D O I：
10.1137/090745465
中图分类号：
F8 [财政、金融];
学科分类号：
0202 ;
摘要：
In this paper, we study the Heston stochastic volatility model in a regime where the maturity is small but large compared to the mean-reversion time of the stochastic volatility factor. We derive a large deviation principle and compute the rate function by a precise study of the moment generating function and its asymptotic. We then obtain asymptotic prices for out-of-the-money call and put options and their corresponding implied volatilities.
引用
收藏
页码：126 / 141
页数：16
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