On the valuation of an option to exchange one interest rate for another

This paper studies the problem of pricing a European option on the difference of two interest rates, which is analogous to an option to exchange one asset for another, studied in Margrabe (1978). It is first shown that such option may be valued as exchanging two interest rates implied in relevant futures prices through an extended Black (1976) model, and then by a two-factor Heath-Jarrow-Morton (HJM) model, which shows that introduction of imperfect interest rates movements is essential for pricing such options, for which a one-factor model such as Ho and Lee (1986) should not be applied.