Malliavin衍生证券衍生品

Jurnal Derivat Pub Date : 2022-11-30 DOI:10.3905/jod.2022.30.2.065

Tom P. Davis

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引用次数: 0

摘要

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。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Malliavin Derivatives of Derivative Securities

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.

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