PT  - JOURNAL ARTICLE
AU  - Tom P. Davis
TI  - Malliavin Derivatives of Derivative Securities
AID  - 10.3905/jod.2022.30.2.065
DP  - 2022 Nov 30
TA  - The Journal of Derivatives
PG  - 65--73
VI  - 30
IP  - 2
4099  - https://pm-research.com/content/30/2/65.short
4100  - https://pm-research.com/content/30/2/65.full
AB  - 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.