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
日本十進分類法
335
出版者
日本経済国際共同センター
出版者別名
Center for International Research on the Japanese Economy
An Asymptotic Expansion with Push-Down of Malliavin Weights
