Parameter Estimation of the Extended Vasiček Model



In this paper, an estimate of the drift and diffusion parameters of the extended Vasiček model is presented. The estimate is based on the method of maximum likelihood. We derive a closed-form expansion for the transition (probability) density of the extended Vasiček process and use the expansion to construct an approximate log-likelihood function of a discretely sampled data of the process. Approximate maximum likelihood estimators (AMLEs) of the parameters are obtained by maximizing the approximate log-likelihood function. The convergence of the AMLEs to the true maximum likelihood estimators is obtained by increasing the number of terms in the expansions with a small time step size.


The extended Vasiček model, transition density, maximum likelihood estimation

Full Text:



O Vasiček. An equilibrium characterization of the term structure. J. Financ. Economet. 1977; 5, 177-88.

J Hull and A White. Pricing interest rate derivative securities. Rev. Financ. Stud. 1990; 3, 573-92.

B Damiano and M Fabio. Interest Rate Models: Theory and Practice, Springer Finance, Heidelberg, 2001, p. 48-60.

SRS Varadhan and WS Daniel. Multidimensional Diffusion Processes, Springer, Heidelberg, 1997, p. 121-35.

S Choi. 2005, Three Essays on Continuous-time Diffusion Models, Ph.D. Dissertation. University of Wisconsin-Madison, United States.

A Egorov, H Li and Y Xu. Maximum likelihood estimation of time inhomogeneous diffusions. J. Econometrics 2003; 114, 107-39.

S Rujivan. Closed-form expansions for transition densities of convenience yield processes. Walailak J. Sci. & Tech. 2009; 6, 127-40.

P Glasserman. Monte Carlo Methods in Financial Engineering, Springer, Heidelberg, 2004, p. 1-36.


  • There are currently no refbacks.

Online ISSN: 2228-835X

Last updated: 12 August 2019