Approximations of Transition Densities for Nonlinear Multivariate Diffusions with an Application to Dynamic Term Structure Models
34 Pages Posted: 21 Mar 2006
Date Written: March 19, 2006
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
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