A Likely Gamma

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.