Simulated Likeliehood Estimation of Diffusions With an Application to the Short Tem Interest Rate
This paper develops a new econometric method to estimate continuous time processes from discretely sampled data. This method extends the maximum likelihood technique to cases where the transition density of the process cannot be computed in closed form but can nevertheless be computed by simulation. The asymptotic properties of the estimator are obtained, showing it to have the same behavior in large samples of the (unknown) true likelihood estimator. That is, the simulated likelihood estimator is consistent and asymptotically normal. The econometric method is used to estimate the parameters of a broad family of processes for the short-term interest rate and test some restrictions to well-known models of the term structure.