Pricing American Interest Rate Claims with Humped Volatility Models

Abstract:     
Some of the most recent empirical studies on interest rate derivatives have found humped shapes in the volatility structure of interest rates. Accordingly, Mercurio and Moraleda (1996) have modeled interest rate dynamics in a way that allows for such a shape in the volatility and is analytically very tractable. Unfortunately, their model cannot be used for pricing American style claims with a recombining lattice. This paper proposes, similarly to Mercurio and Moraleda (1996), a humped volatility of interest rates model that not only gives explicit formulas for European options on discount bonds but also allows for pricing American options in a recombining lattice. In fact, it can be embedded in either the Hull and White (1993, 1994, 1995) tree or the Li, Ritchken and Sankarasubramanian (1995) lattice. The paper shows, furthermore, that if a deterministic volatility model can be embedded in either of these algorithms then so does it in the other one. It is also proved that it is not possible to find a volatility of the class proposed by Mercurio and Moraleda (1996) such that American style claims can be priced using a Markovian process for the spot rate.

JEL Classification: G13, E43

working papers series