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.
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