{"title":"Malliavin Derivatives of Derivative Securities","authors":"Tom P. Davis","doi":"10.3905/jod.2022.30.2.065","DOIUrl":null,"url":null,"abstract":"The Malliavin calculus has been used successfully to derive efficient formulas for delta and gamma. This article extends these results to all higher-order spatial derivatives with respect to the underlying asset for arbitrary payoffs in both the Black-Scholes (Black and Scholes 1973) (lognormal) and Bachelier (normal) models. The former reproduces a well-known result from Peter Carr (2000), whereas the latter extends this work to the normal case.","PeriodicalId":34223,"journal":{"name":"Jurnal Derivat","volume":"30 1","pages":"65 - 73"},"PeriodicalIF":0.0000,"publicationDate":"2022-11-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Jurnal Derivat","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.3905/jod.2022.30.2.065","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
The Malliavin calculus has been used successfully to derive efficient formulas for delta and gamma. This article extends these results to all higher-order spatial derivatives with respect to the underlying asset for arbitrary payoffs in both the Black-Scholes (Black and Scholes 1973) (lognormal) and Bachelier (normal) models. The former reproduces a well-known result from Peter Carr (2000), whereas the latter extends this work to the normal case.
Malliavin微积分已被成功地用于推导有效的delta和gamma公式。本文将这些结果推广到Black-Scholes（Black and Scholes 1973）（lognormal）和Bachelier（normal）模型中任意收益的所有关于基础资产的高阶空间导数。前者再现了彼得·卡尔（2000）的一个著名结果，而后者将这项工作扩展到了正常情况。
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