Term Structure Movements and Pricing Interest Rate Contingent Claims

This paper derives an arbitrage-free interest rate movements model (AR model). This model takes the complete term structure as given and derives the subsequent stochastic movement of the term structure such that the movement is arbitrage free. We then show that the AR model can be used to price interest rate contingent claims relative to the observed complete term structure of interest rates. This paper also studies the behavior and the economics of the model. Our approach can be used to price a broad range of interest rate contingent claims, including bond options and callable bonds. INTEREST RATE OPTIONS, CALLABLE bonds, and floating rate notes are a few examples of interest rate contingent claims. They are characterized by their finite lives and their price behavior, which crucially depends 'on the term structure and its stochastic movements. In recent years, with the increase in interest rate volatility and the prevalent use of the contingent claims, the pricing of these securities has become a primary concern in financial research. The purpose of this paper is to present a general methodology to price a broad class of interest rate contingent claims. The crux of the problem in pricing interest rate contingent claims is to model the term structure movements and to relate the movements to the assets' prices. Much academic literature has been devoted to this problem. One earlier attempt is that of Pye [15]. He assumed that the interest rates move according to a (Markov) transition probabilities matrix, and he then used the expectation hypothesis to price the expected cash flow of the asset-in his case, a callable bond (Pye [16]). Recently, investigators have focused more on developing equilibrium models. Cox, Ingersoll, and Ross (CIR) [7] assumed that the short rate follows a meanreverting process. By further assuming that all interest rate contingent claims are priced contingent on only the short rate, using a continuous arbitrage argument they derived an equilibrium pricing model. Brennan and Schwartz (BS) [2] extended the CIR model to incorporate both short and long rates and studied the pricing of a broad range of contingent claims (BS [1, 3]). In these * New York University Graduate School of Business Administration and Korea Economic Research Institute, respectively. This paper contains results presented in an earlier paper entitled "Term Structure Movements and the Pricing of Corporate Bonds Provisions," May 1985, Salomon Brothers Center, New York University. We would like to thank Michael Brennan, Bill Carleton, Georges Courtadon, Art Djang, Steve Figlewski, Bob Geske, David Jacob, In Joon Kim, and Eduardo Schwartz for their helpful comments on the earlier version of the paper. We would also like to thank, in particular, the referee, Eduardo Schwartz, for many of his helpful comments on this paper. We are responsible for the remaining errors.