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

Farmer, Leland and Toda, Alexis Akira (2016): Discretizing Nonlinear, Non-Gaussian Markov Processes with Exact Conditional Moments. Forthcoming in: Quantitative Economics

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.

• Item Type: MPRA Paper
• Language: English
• Keywords: asset pricing models, duality, Kullback-Leibler information, numerical methods, solution accuracy
• Subjects: C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C63 - Computational Techniques ; Simulation Modeling; C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C68 - Computable General Equilibrium Models; G - Financial Economics > G1 - General Financial Markets > G12 - Asset Pricing ; Trading Volume ; Bond Interest Rates

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