ON DIFFUSION-APPROXIMATION OF SOME TERM STRUCTURE MODELS

Studying various term structure models has become a very important issue in financial research. In this work, we take the approach of classifying the underlying models with respect to the time parameter involved as a point of departure, and describe the connections among these models (discrete vs. continuous). Our goal is to show that the discrete and continuous models axe not all isolated. They are closely related through limit processing. To illustrate, we take Ho-Lee's model as a prototype example. In lieu of using the commonly employed PDE (partial differential equation) approach, we show that an appropriate continuous time interpolation leads to a diffusion limit by using the weak- convergence methods. In addition, equivalence between the interest rate models and discounted price models axe also established.