Ho ＆ Lee(1986) derived an arbitrage-free interest rate movements model (AR model). Their model took the complete term structure as given and derived the subsequent stochastic movement of the term structure such that the movement is arbitrage free. They then showed that the AR model can be used to price interest rate contingent claims relative to the observed complete term structure of interest rates. But, Bliss ＆ Ronn (1989) performed diagonostic tests on the data to demonstrate that the empirical results reject a binomial model in favor of a trinomial one.
Therefore, this paper drives new arbitrage based model (TAR model). The assumptions of TAR model are the same as those of AR model only except to assume the trinomial process to postulate the uncertainty of bond prices. Then, this paper shows that TAR model can be used to price interest rate contingent claims and that TAR model belongs to the one-factor model.
