Interest Rate Option Pricing with Volatility Humps

This paper develops a simple model for pricing interest rate options. Analytical solutions are developed for European claims and extremely efficient algorithms exist for tile pricing of American options. The interest rate claims are priced in the Heath-Jarrow-Morton paradigm, and hence incorporate full information on the term structure. The volatility structure for forward rates is humped, and includes as a special case the exponentially dampened volatility structure used in tile Generalized Vasicek model. The structure of volatilities is captured without using time varying parameters. As a result, the volatility structure is stationary. It is not possible to have all the above properties hold in a Heath Jarrow Morton model with a single state variable. It is shown that the full dynamics of the term structure can, however, be captured by a three state Markovian system. As a result, simple path reconnecting lattices cannot be constructed to price American claims. Nonetheless, we provide extremely efficient lattice based algorithms for pricing claims, which rely on carrying small matrices of information at each node. Empirical support for the models developed are provided.