Short-Term At-the-Money Asymptotics under Stochastic Volatility Models

被引：26

作者：

El Euch, Omar ^{[1
]}

Fukasawa, Masaaki ^{[2
]}

Gatheral, Jim ^{[3
]}

Rosenbaum, Mathieu ^{[4
]}

机构：

[1] Ecole Polytech, F-91128 Palaiseau, France

[2] Osaka Univ, Grad Sch Engn Sci, Osaka 5608531, Japan

[3] CUNY Bernard M Baruch Coll, Dept Math, 17 Lexington Ave, New York, NY 10010 USA

[4] Ecole Polytech, CMAP, F-91128 Palaiseau, France

来源：

SIAM JOURNAL ON FINANCIAL MATHEMATICS | 2019年 / 10卷 / 02期

关键词：

asymptotic expansion; implied volatility; rough volatility; IMPLIED VOLATILITY; MALLIAVIN CALCULUS; BEHAVIOR; FORMULA; SKEW;

D O I：

10.1137/18M1167565

中图分类号：

F8 [财政、金融];

学科分类号：

0202 ;

摘要：

A small-time Edgeworth expansion of the density of an asset price is given under a general stochastic volatility model, from which asymptotic expansions of put option prices and at-the-money implied volatilities follow. A limit theorem for at-the-money implied volatility skew and curvature is also given as a corollary. The rough Bergomi model is treated as an example.

引用

页码：491 / 511

页数：21

共 23 条

[1] On the short-time behavior of the implied volatility for jump-diffusion models with stochastic volatility [J].