The Valuation of Interest Rate Derivatives in a Multi-Factor Term Structure Model with Deterministic Components

In this paper, the multi-factor Cox, Ingersoll, Ross (CIR) model of the term structure is extended by adding a deterministic component to the interest rate equation. This extra component makes the model flexible enough to match any initial term structure, while retaining the other features of the multi-factor CIR model. Current values for the random state variables can be set so that the model provides a good fit to the term structure, and the deterministic component can be used to fine tune the model for an exact fit. The model has nonnegative interest rates and relies on several random factors to capture the potential variability of the term structure, and it is easy to implement. In the paper, I present fast, closed form solutions for forward rates, futures rates, and several European interest rate options. Numerical methods for pricing other more complex interest rate derivatives are easy to implement because the model is Markovian; the distribution for interest rates each period depends on the current values for the state variables that determine the instantaneous interest rate. An important consequence of this feature is that nodes in a lattice model recombine. The paper also includes an application in which the model is calibrated to initial term structures in both the Treasury market and the Eurodollar futures market.