Data-based Automatic Discretization of Nonparametric Distributions

TL;DR

This paper introduces a nonparametric method for discretizing data distributions using Gaussian quadrature, improving economic modeling accuracy by avoiding parametric assumptions and revealing significant portfolio misestimations.

Contribution

It presents a novel nonparametric calibration technique based on the Golub-Welsch algorithm for economic models, replacing traditional parametric assumptions.

Findings

Nonparametric calibration affects portfolio weightings significantly.

Assuming Gaussian shocks can lead to 17% overweighting in stocks.

Method improves the accuracy of economic distribution modeling.

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.