Discretizing Nonlinear, Non-Gaussian Markov Processes with Exact Conditional Moments

Quantitative Economics, July 2017, Volume 8, Issue 2, pp. 651-683

50 Pages Posted: 28 Mar 2015 Last revised: 31 Aug 2017

See all articles by Leland Farmer

Leland Farmer

University of Virginia

Alexis Akira Toda

University of California, San Diego (UCSD) - Department of Economics

Date Written: October 26, 2016

Abstract

Approximating stochastic processes by finite-state Markov chains is useful for reducing computational complexity when solving dynamic economic models. We provide a new method for accurately discretizing general Markov processes by matching low order moments of the conditional distributions using maximum entropy. In contrast to existing methods, our approach is not limited to linear Gaussian autoregressive processes. We apply our method to numerically solve asset pricing models with various underlying stochastic processes for the fundamentals, including a rare disasters model. Our method outperforms the solution accuracy of existing methods by orders of magnitude, while drastically simplifying the solution algorithm. The performance of our method is robust to parameters such as the number of grid points and the persistence of the process.

Keywords: asset pricing models, duality, Kullback-Leibler information, numerical methods, solution accuracy

JEL Classification: C63, C68, G12

Suggested Citation

Farmer, Leland and Toda, Alexis Akira, Discretizing Nonlinear, Non-Gaussian Markov Processes with Exact Conditional Moments (October 26, 2016). Quantitative Economics, July 2017, Volume 8, Issue 2, pp. 651-683. Available at SSRN: https://ssrn.com/abstract=2585859 or http://dx.doi.org/10.2139/ssrn.2585859

Leland Farmer

University of Virginia ( email )

237 Monroe Hall
P.O. Box 400182
Charlottesville, VA 22904-418
United States

Alexis Akira Toda (Contact Author)

University of California, San Diego (UCSD) - Department of Economics ( email )

9500 Gilman Drive
Mail Code 0508
La Jolla, CA 92093-0508
United States

HOME PAGE: http://https://sites.google.com/site/aatoda111/

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