Journal of Banking and Finance 17 (1993) 107991095. North-Holland The analysis and valuation of interest rate options R.C. Stapleton Unioersity of Luncuster. Lancuster, LAI IYX, UK and EIASM, Brussels, Belgium M.G. Subrahmanyam Stern School of Business, New York Universily, New York, NY 10006, USA Received October 1991, linal version received October 1992 This paper provides a simple, alternative model for the valuation of European-style interest rate options. The assumption that drives the hedging argument in the model is that the forward prices of bonds follow an arbitrary two-state process. Later, this assumption is made more specific by postulating that the discount on a zero-coupon bond follows a multiplicative binomial process. In contrast to the BlackkScholes assumption applied to zero-coupon bonds, the limiting distribution of this process has the attractive features that the zero-bond price has a natural barrier at unity (thus precluding negative interest rates), and that the bond price is negatively skewed. The model is used to price interest rate options in general. and interest rate caps and floors in particular. The model is then generalized and applied to European-style options on bonds. A relationship is established between options on swaps and options on coupon bonds. The generalized model then provides a computationally simple formula, closely related to the Black-Scholes formula, for the valuation of European-style options on swaps. Key words: Interest rate options: Swap options: Valuation JEL zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA c ~la ss$c a tio n: 6 I3 1. Introduction In this paper, we propose an alternative model, which is computationally simple, for the valuation of European style interest rate options. Options on interest rates, such as interest rate caps and floors, and swap options, are first converted into equivalent options on bonds. We then assume that the bond discount is lognormally distributed. It is then shown that a transformation of the Black and Scholes (1973) (BS) formula can be used to value the options. Our model has many features in common with existing models in the literature. As in the case of the models suggested by Merton (1973), Turnbull and Milne (1991) Hull and White (1990) Jamshidian (1989) and Satchel1 Correspondence IO: Professor Richard C. Stapleton, Department of Accounting and Finance, University of Lancaster. Lancaster LA1 4YX. UK. 03784266/93/$06.00 $> 1993-Elsevier Science Publishers B.V. All rights reserved