Maximum Likelihood Estimation of Time-Inhomogeneous Diffusions
Posted: 17 Sep 2002
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Maximum Likelihood Estimation of Time-Inhomogeneous Diffusions
Abstract
We extend the maximum likelihood estimation method of Ait-Sahalia (2002) for time-homogeneous diffusions to time-inhomogeneous ones. We derive a closed-form approximation of the likelihood function for discretely sampled time-inhomogeneous diffusions, and prove that this approximation converges to the true likelihood function and yields consistent parameter estimates. Monte Carlo simulations for several financial models reveal that our method largely outperforms other widely used numerical procedures in approximating the likelihood function. Furthermore, parameter estimates produced by our method are very close to the parameter estimates obtained by maximizing the true likelihood function, and superior to estimates obtained from the Euler approximation.
Keywords: Maximum likelihood estimation, time-inhomogeneous diffusion, transition density, Hermite expansion
JEL Classification: C0, C1, C4, G0
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