Simulated Greeks for American Options

Abstract

This paper considers estimation of price sensitivities, so-called Greeks, for American style options using flexible simulation methods combined with initial dispersed state variables. The asymptotic properties of the estimators are studied and convergence of the method is established under mild regularity conditions. A 2-step method is proposed with an adaptive choice of optimal initially dispersed state variables, that controls and balances off the bias of the estimates against their variance. Numerical results show that the method works extremely well for very reasonable choices of spread sizes, regressors, and simulated paths and demonstrate that the proposed method compares well to existing alternatives.

Keywords: Hedging, Least Squares Monte Carlo method, Price sensitivities

JEL Classification: C15, G12, G13