金融产品定价之一利率模型.pdf

文档介绍：The General Hull-White Model and Super Calibration
John Hull and Alan White

Joseph L. Rotman School of Management
University of Toronto
105 St e Street
Toronto, Ontario M5S 3E6
Canada
Tel: [phone] (Hull)
Tel: [phone] (White)
August, 2000
The General Hull-White Model and Super Calibration
There are two major approaches to modeling the term structure of interest rates. One
approach is to model the evolution of either forward rates or discount bond prices. This
approach was first developed by Heath, Jarrow and Morton (HJM, 1992). In 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 plex 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 non-
instantaneous forward rates. This modification e 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 putationally 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 understan