文档介绍：Heath, Jarrow, and Morton Interest Rate Modelling Using
ponent Analysis'
Cedreece Tamagushiku
March, 2006
This finc590 is put forward as part of requirements of the Master of Business degree at the University
of Otago. Many thanks must be given to Dr. Alan Stent for his guidance, patience and supervision of
this research.
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Jarrow
1. Morton Interest Rate Modelling Using Principal
Component Analysis
Cedreece Tamagushiku
Abstract
The purpose of this paper is to investigate the performance of three different models
in the pricing of call options on y-day bank bill futures traded on the Sydney
Futures Exchange between 1993 and 2000. The three models analysed are embedded
into the Heath, Jarrow, and Morton framework namely; the one, two, and three factor
models. ponents Analysis was applied in order to provide the forward
rate volatility functions necessary to implement several popular multi-factor versions
of the Heath, Jarrow, and Morton model. Results showed that the three-factor model
consistently outperforms the one and two-factor models. Also the pricing errors are
positively correlated with the time to maturity of the option and that no real
relationship existed between the errors of one and two-factor models and the date and
the moneyness of the options. Although three-factor models exhibited lower errors as
time progressed.
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3. ponent Analysis ............. ............................................................ --------------------------'7 7
ponent Properties ------------------------.0
4. Heath, Jarrow, and Morton Framework .......... .......................................................... 9
Parameter Estimation .................................................. ................ . ........ . ..... 10
One-Factor Model ...... ...... . ........ 10
Two and Three-Factor Models ............................... ...................................... 10
5. The Sydney Futures Exchange ................