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Data-Based Automatic Discretization of Nonparametric Distributions

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  • Alexis Akira Toda

    (University of California San Diego)

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.

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  • Alexis Akira Toda, 2021. "Data-Based Automatic Discretization of Nonparametric Distributions," Computational Economics, Springer;Society for Computational Economics, vol. 57(4), pages 1217-1235, April.
    • Handle: RePEc:kap:compec:v:57:y:2021:i:4:d:10.1007_s10614-020-10012-6
    DOI: 10.1007/s10614-020-10012-6
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