.ISSN (e) 1759-7331
(print) 1759-7323
Quantitative Economics
An open-access journal in quantitative economics
Journal of the
Econometric Society
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Quantitative Economics, Volume 8, Issue 2 (July 2017)

Discretizing nonlinear, non‐Gaussian Markov processes with exact conditional moments

Leland E. Farmer, Alexis Akira Toda

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.

Asset pricing models duality Kullback–Leibler information numerical methods solution accuracy C63 C68 G12

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