Data‑based Automatic Discretization of Nonparametric Distributions

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 (Golub and Welsch in Math Comput 23(106): 221–230, 1969. https://doi.org/10.1090/S0025-5718-69-99647 -1) for Gaussian quadrature. Applications to an asset pricing model and an optimal portfolio problem suggest that assuming normal instead of nonparametric shocks leads to up to 8% reduction in the equity premium and 17% overweighting in the stock portfolio because the investor underestimates the probability of crashes.

Toda A. (2020) Data‑based Automatic Discretization of Nonparametric Distributions. Computational Economics.