A Two-factor Interest Rate Model and Contingent Claims Valuation

gent claims. The ~wo factors are the instantaneous riskless (short-term) interest rate and the instantaneous variance of changes in this short-term interest rate. The model is attractive not only because it provides for closed form expressions in a two-factor world. but also because it explicitly allows for a stochastic volatility f.lctOr. As the parameters of the model can be estimated using both time series and cross sections of prices (or yields), the framework provides reasonable dynamics of the factors or state variables. [n this article we extend the Longstaff-Schwartz model to allow it to fit the initial discount function exactly. We do this by simply deriving a partial differentia] equation for forward prices and using the actual discount factors to obtain the present value of the forward prices. This method can then be used for valuing all European interest rate-contingent claims. This extension of the model cannot be used to price discount bonds because by construction all discount bonds used exactly fit the model, I but it has the advantage of using all the information in the current term structure to price interest rate-contingent claims within the framework of the two-f.1Ctor model.