Simulated Greeks for American options

Abstract

This paper develops a method to estimate price sensitivities, so-called Greeks, for American style options using flexible simulation methods combined with initially dispersed state variables. The asymptotic properties of the estimators are studied, and convergence of the method is established. A 2-stage method is proposed with an adaptive choice of optimal dispersion of state variables, which controls and balances off the bias of the estimates against their variance. Numerical results show that the method compares exceptionally well to existing alternatives, works well for very reasonable choices of dispersion sizes, regressors, and simulated paths, and it is robust to choices of these parameters. We apply the method to models with time varying volatility, demonstrating that there are large differences between estimated Greeks with affine and non-affine models, that Greeks vary significantly through periods of crisis, and that the errors made when using Greeks implied from, e.g. misspecified models with constant volatility can be extremely large.