On the Discrete Time and Continuous States Models

Abstract

W~e shall consider a discrete time version of Vasicek (1977) model with continuous state space. Unlike traditional approaches, we regard that continuous time and states models are'approximation to the real discrete time models. This may be justified by the fact that we can only observe price of every asset in discrete time domain. In order to analyze discrete time and continuous state models, we shall modify the Ito formula so that it is suitable for the discrete time models. Using the modified Ito formula by Rao et al. (1974), we shall obtain the PDE for the continuous time approximation of the time t price of T maturity default free zero coupon bonds up to the terms as small as 1/~:, where h denotes the atom of time interval.