Conditional Estimation of Diffusion Processes

There are a number of circumstances in finance where it is useful to estimate diffusion processes conditional on some event. In this paper, we develop the theoretical and numerical tools necessary to perform conditional estimation of diffusion processes within a generalized method of moments framework. We illustrate our method by estimating a univariate diffusion process for a standard time-series of interest rate data conditioned to remain between lower and upper boundaries. A test statistic fails to reject by a wide margin the linearity of the conditionally estimated drift coefficient.