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Working Paper

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.

Working Papers of the Federal Reserve Bank of Cleveland are preliminary materials circulated to stimulate discussion and critical comment on research in progress. They may not have been subject to the formal editorial review accorded official Federal Reserve Bank of Cleveland publications. The views expressed in this paper are those of the authors and do not represent the views of the Federal Reserve Bank of Cleveland or the Federal Reserve System.

Suggested Citation

Ritchken, Peter, and Iyuan Chuang. 1997. “Interest Rate Option Pricing with Volatility Humps.” Federal Reserve Bank of Cleveland, Working Paper No. 97-14.