Pricing American interest rate claims with humped volatility models

Some of the most recent empirical studies on interest rate derivatives have found humped shapes in the volatility structure of interest rates. In this paper, we propose a simple model that allows for humped volatility structures, and that can be described by one state variable. With the model, American style claims can be priced very efficiently which is very important if the model has to be calibrated daily to market prices of standard American options. Furthermore, the model allows for explicit formulas for European style options. Finally, the computational efficiency of our model in the Li et al. (1995) framework is compared with the efficiency in a typical Hull and White (1993a, 1994, 1996) framework. In fact, we can use both procedures for our model, since we prove that if a deterministic volatility model can be embedded in either of these algorithms, then so it does in the other one. Empirical evidence from option data supporting our model is provided as well.