アイテムタイプ

テクニカルレポート / Technical Report

言語

英語

キーワード

Malliavin calculus, Asymptotic expansion, Stochastic volatility, Implied volatility, Local volatility, Shifted log-normal model, Jump-diffusion model, Integration-by-parts, Malliavin weight, Push-down, Bismut identity

著者

Takahashi Akihiko
Yamada Toshihiro

著者所属

Graduate School of Economics, the University of Tokyo
Mitsubishi UFJ Trust Investment Technology Institute Co.,Ltd. (MTEC)

抄録

This paper derives asymptotic expansion formulas for option prices and implied volatilities as well as the density of the underlying asset price in a stochastic volatility model. In particular, the integration-by-parts formula in Malliavin calculus and the push-down of Malliavin weights are effectively applied, which provides an expansion formula for generalized Wiener functionals and the closed-form approximation formulas in stochastic volatility environment. In addition, it presents applications of the general formula to a local volatility expansion in the stochastic volatility model and expansions of option prices in the shifted log-normal and jump-diffusion models with stochastic volatilities. Finally, with an application of the Bismut identity the paper shows an expansion of the solution to the partial differential equation for pricing in a stochastic volatility model.

内容記述

Revised in January 2010, August 2010 and April 2011
本文フィルはリンク先を参照のこと

雑誌名

Discussion paper series. CIRJE-F

巻

CIRJE-F-695

発行年

2009-12

書誌レコードID

AA11450569

フォーマット

application/pdf