Data-Based Automatic Discretization of Nonparametric Distributions

Alexis Akira Toda

Computational Economics, 2021, vol. 57, issue 4, No 11, 1217-1235

Abstract: 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 (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.

Keywords: Calibration; Discrete approximation; Gaussian quadrature (search for similar items in EconPapers)
Date: 2021
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Working Paper: Data-based Automatic Discretization of Nonparametric Distributions (2019)
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DOI: 10.1007/s10614-020-10012-6

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