Data-based Automatic Discretization of Nonparametric Distributions

Abstract

Although using non-Gaussian distributions in economic models has become increasingly popular, currently there is no systematic way for calibrating a discrete distribution from the data without imposing parametric assumptions. This paper proposes a simple nonparametric calibration method based on the Golub-Welsch algorithm for Gaussian quadrature. Application to an optimal portfolio problem suggests that assuming Gaussian instead of nonparametric shocks leads to up to 17% overweighting in the stock portfolio because the investor underestimates the probability of crashes.