The General Hull-White Model and Super Calibration

this paper they model the behavior of instantaneous forward rates. The method is both powerful (it contains many other term structure models as special cases) and easy to understand. It exactly fits the initial term structure of interest rates, it permits as complex a volatility structure as desired, and it can readily be extended to as many sources of risk as desired. More recently the HJM model has been modified by Brace, Gatarek and Musiella (1997), Jamshidian (1997), and Miltersen, Sandmann, and Sondermann (1997) to apply to noninstantaneous forward rates. This modification has come to be known as the Libor Market Model (LMM). In one version, 3-month forward rates are modeled. This allows the model to exactly replicate observed cap prices that depend on 3-month forward rates. In another version forward swap rates are modeled. This allows the model to exactly replicate observed European swap option prices. The main difficulty with the HJM -- LMM models is that they are difficult to implement by any means other then Monte Carlo simulation. As a result they are computationally slow and difficult to use for American or Bermudan style options. The other major approach to modeling the term structure is to describe the evolution of the instantaneous rate of interest, the rate that applies over the next short interval of time. Short rate models are often more difficult to understand than models of the forward rate. However, they are implemented in the form of a recombining tree similar to the stock price tree first developed by Cox, Ross, and Rubinstein (1979). This makes them computationally fast and useful for valuing all types of interest-rate derivatives. The Generalized Model The generalized Hull-White model is a model in which some function of the short-rate obeys a ..