TY - JOUR T1 - Malliavin Derivatives of Derivative Securities JF - The Journal of Derivatives SP - 65 LP - 73 DO - 10.3905/jod.2022.30.2.065 VL - 30 IS - 2 AU - Tom P. Davis Y1 - 2022/11/30 UR - https://pm-research.com/content/30/2/65.abstract N2 - 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. ER -