Simulated Likelihood Estimation of Diffusions with an Application to Exchange Rate Dynamics in Incomplete Markets

We present an econometric method for estimating the parameters of a diffusion model from discretely sampled data. The estimator is transparent, adaptive, and inherits the asymptotic properties of the generally unattainable maximum likelihood estimator. We use this method to estimate a new continuous-time model of the Joint dynamics of interest rates in two countries and the exchange rate between the two currencies. The model allows financial markets to be incomplete and specifies the degree of incompleteness as a stochastic process. Our empirical results offer several new insights into the dynamics of exchange rates.