Approximations of Transition Densities for Nonlinear Multivariate Diffusions with an Application to Dynamic Term Structure Models

34 Pages Posted: 21 Mar 2006

See all articles by Paul Schneider

Paul Schneider

University of Lugano - Institute of Finance; Swiss Finance Institute

Date Written: March 19, 2006

Abstract

Approximations to transition densities are needed for estimation of most multivariate diffusion models used in finance. I test a variety of proxies within Markov chain Monte Carlo estimation of a multivariate term structure model with nonlinear dynamics. Realistic parameters for the simulation experiments are obtained from estimation on monthly US interest rate data. The resulting processes are close to being explosive under the pricing probability measure. A simple Gauss proxy performs surprisingly well. Closed-form likelihood expansions exhibit the best results with respect to parameter estimates and computational speed. A full Bayesian approach together with importance sampling promises to be very well suited for larger-dimensional problems.

Keywords: Multivariate Nonlinear Diffusion, Estimation, MCMC

JEL Classification: C11,C15,C52

Suggested Citation

Schneider, Paul Georg, Approximations of Transition Densities for Nonlinear Multivariate Diffusions with an Application to Dynamic Term Structure Models (March 19, 2006). Available at SSRN: https://ssrn.com/abstract=892234 or http://dx.doi.org/10.2139/ssrn.892234

Paul Georg Schneider (Contact Author)

University of Lugano - Institute of Finance ( email )

Via Buffi 13
CH-6900 Lugano
Switzerland

Swiss Finance Institute ( email )

c/o University of Geneva
40, Bd du Pont-d'Arve
CH-1211 Geneva 4
Switzerland

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