2020-09-24T05:50:07Zhttps://repository.dl.itc.u-tokyo.ac.jp/?action=repository_oaipmhoai:repository.dl.itc.u-tokyo.ac.jp:000428522020-09-08T01:26:09Z00062:07433:0743400009:07435:07436
An Asymptotic Expansion with Push-Down of Malliavin WeightsengMalliavin calculusAsymptotic expansionStochastic volatilityImplied volatilityLocal volatilityShifted log-normal modelJump-diffusion modelIntegration-by-partsMalliavin weightPush-downBismut identityhttp://hdl.handle.net/2261/32439Technical ReportTakahashi, AkihikoYamada, ToshihiroThis 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.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Discussion paper series. CIRJE-FCIRJE-F-6952009-12AA11450569application/pdf335日本経済国際共同センターhttp://www.cirje.e.u-tokyo.ac.jp/research/dp/2009/2009cf695ab.html2017-06-16