Likelihood Ratio Method and Algorithmic Differentiation: Fast Second Order Greeks

Abstract

We show how Adjoint Algorithmic Differentiation can be combined with the so-called Pathwise Derivative and Likelihood Ratio Method to construct efficient Monte Carlo estimators of second order price sensitivities of derivative portfolios. We demonstrate with a numerical example how the proposed technique can be straightforwardly implemented to greatly reduce the computation time of second order risk.

Keywords: Adjoint Algorithmic Differentiation, Likelihood Ratio Method, Derivatives Pricing, Pathwise Derivative Method, Monte Carlo