Markovian Term Structure Models

Patrick Hagan - Banque Paribas and Diana E. Woodward - CSA Inc.

We present a general procedure for creating Markovian term structure models. All "n state variable" models that are created by this procedure are a subclass of the n factor HJM models and fit the initial term structure exactly. Therefore they are arbitrage free. Because they have only one state variable per factor, two- and even three-factor models can be computed efficiently, without resorting to Monte Carlo techniques. This computational efficiency makes calibration of the new models to market prices relatively straightforward. Extended Hull-White, extended CIR, Black-Karasinski, Jamshidian's Brownian path independent models, and Flesaker's rational log normal models are one-state variable models which fit naturally within our theoretical framework. The "separable" n-factor models of Ritchken and Sankarasubramanian and of Cheyette which require n(n+3)/2 state variables — are degenerate members of the new class of models with n(n+3)/2 factors. We use one-state variable models to illustrate the theory. We focus on the B-n models, a. class of exactly "solvable" models, and show how these models can be calibrated efficiently to market prices of swaptions and caplets.

Scheduled for Session 5.4 Computational Finance