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
Date Written: October 26, 2016
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
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