A Likely Gamma

11 Pages Posted: 25 Nov 2020 Last revised: 9 Jan 2021

See all articles by Tom P. Davis

Tom P. Davis

FactSet Research Systems Inc.

Date Written: October 9, 2020

Abstract

Automatic differentiation is now used extensively in finance to determine the greeks of financial securities. Unfortunately when using this technique with binomial trees the second order sensitivities, such as gamma, cannot be calculated due to the interaction of the structure of the lattice and singularities in the derivatives of payoff functions. In this paper we use recent results on the likelihood ratio method on binomial trees to overcome this issue. The algorithm for determining delta via the likelihood ratio method is extremely easy and efficient to implement, and when combined with automatic differentiation yields continuous gammas.

Keywords: Likelihood ratio method, Binomial tree, Green's function, Quantitative Finance, Automatic Differentiation

JEL Classification: C60, C63

Suggested Citation

Davis, Tom, A Likely Gamma (October 9, 2020). Available at SSRN: https://ssrn.com/abstract=3708483 or http://dx.doi.org/10.2139/ssrn.3708483

Tom Davis (Contact Author)

FactSet Research Systems Inc. ( email )

601 MERRIT 7 #3
NORWALK, CT 06851
United States

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