We model the term-structure modeling of interest rates by considering the forward rate as the solution of a stochastic hyperbolic partial differential equation. First, we study the arbitrage-free model of the term structure and explore the completeness of the market. We then derive results for the pricing of general contingent claims. Finally we obtain an explicit formula for a forward rate cap in the Gaussian framework from the general results.

We consider a slight perturbation of the Hull-White short rate model and the resulting modified forward rate equation. We identify the model coefficients by using the martingale property of the normalized bond price. The forward rate and the system parameters are then estimated by using the maximum likelihood method.

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