Review of synthesis of no-arbitrage Gaussian term structure models

This paper provides a general approach to deriving no-arbitrage Gaussian term structure models with a threefold contribution. First, we present a general relationship between the short rate, forward rates, and futures rates, and apply it to derive no-arbitrage Gaussian term structure models. We show two examples, the extended-Vasicek model of Hull and White (1990) and the two-factor model of Hull and White (1994b), in order to demonstrate the derivation procedure. Although many results presented in this article are not new to the literature, our methodology is simple, straightforward, and provides intuitive explanations. Second, our analysis fills a gap in the understanding of the relationship between the short rate process and the forward rate process, and thus provides a linkage between Heath, Jarrow, and Morton's (1990, 1992) model and Hull and White's (1990) model. Therefore, this paper contributes pedagogical value to the term structure model literature. Third, as our models use discrete time setting, it is relatively easy to implement them with numerical procedures such as the lattice approach or Monte Carlo simulations so as to price interest rate derivatives. We give numerical examples to show how to elaborate on the numerical procedure of Hull and White (1994a) using our discrete time model.