The authors derive a unified model that gives closed form solutions for caps and floors written on interest rates as well as puts and calls written on zero-coupon bonds. The crucial assumption is that simple interest rates over a fixed finite period that matches the contract, which the authors want to price, are log-normally distributed. Moreover, this assumption is shown to be consistent with the Heath-Jarrow-Morton model for a specific choice of volatility.

ABSTRACT We derive a unified model that gives closed form solutions for caps and floors written on interest rates as well as puts and calls written on zero‐coupon bonds. The crucial assumption is that simple interest rates over a fixed finite period that matches the contract, which we want to price, are log‐normally distributed. Moreover, this assumption is shown to be consistent with the Heath‐Jarrow‐Morton model for a specific choice of volatility.

Kristian R. Miltersen, Klaus Sandmann, Dieter Sondermann, Closed Form Solutions for Term Structure Derivatives with Log-Normal Interest Rates, The Journal of Finance, Vol. 52, No. 1 (Mar., 1997), pp. 409-430