Multivariate Markov Chain Approximations

25 Pages Posted: 11 Mar 2013

See all articles by Simon Scheuring

Simon Scheuring

University of Zurich - Department of Banking and Finance

Benjamin Jonen

University of Zurich

Date Written: March 10, 2013


To solve equilibrium models numerically, it is necessary to discretize vector autoregressive processes (VAR) into a finite number of states. Univariate Markov chain approximations are well studied, however, few papers address the multivariate case. This paper presents three approaches to the problem: quadrature, moment matching and bin estimation.

Quadrature uses numerical integration schemes over the conditional distribution of the error terms. Moment matching replicates the first moments of the VAR. Bin estimation segments the data into bins and estimates the transition probabilities with maximum likelihood.

A comparative study in a standard asset pricing model shows that quadrature has difficulties when the model involves only few states, bin estimation fares better, while moment matching delivers the smallest errors. However, an experiment demonstrates the convincing results of moment matching to be double-edged. The introduction of a disaster state permits to alter model results despite matching all first and second moments.

Keywords: Markov chain approximation, Asset Pricing, Macroeconomics, Dynamic Programming

JEL Classification: C63, E44, G12

Suggested Citation

Scheuring, Simon and Jonen, Benjamin, Multivariate Markov Chain Approximations (March 10, 2013). Available at SSRN: or

Simon Scheuring

University of Zurich - Department of Banking and Finance ( email )

Schönberggasse 1
Zürich, 8001

Benjamin Jonen (Contact Author)

University of Zurich ( email )

Rämistrasse 71
Zürich, CH-8006

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