Consider extending the model specification to allow for a time-dependent drift parameter. Hence the short- term interest rate dynamics become:

Due to the Markovian nature of the model, we assume that all information about past movements and expectations of future movements is contained in the current ( observed ) term structure. Therefore the functional form of the time-dependent parameter ( * t * ), may be determined from observed bond prices and the values of the constant parameters. No prior restrictions are placed on the functional form of ( * t * ) since it is determined so as to reflect the specific observed term structure.

Consider the conditional expectation of * r * ( * s * ) with the time-dependent parameter ( * t * ). Following the methodology of §(2.7.1) we have the integral form of the short-term interest rate process:

Taking expectations and differentiating with respect to * s * produces:

so, integrating over [ * t, s * ] gives the conditional expectation of * r * ( * s * )as:

The bond price takes the same functional form as specified in (2.27), with a modification to one of the parameters as depicted below:

where:

Given this formulation of the bond price and the observed term structure, (2.44) can be solved for ( * s * ) for all * s * ˆˆ [ * t, T * ] which could then be used in conjunction with (2.41) to determine future expectations of the short-term interest rate as specified by the current observed term structure.

Interest Rate Modelling (Finance and Capital Markets Series)

ISBN: 1403934703

EAN: 2147483647

EAN: 2147483647

Year: 2004

Pages: 132

Pages: 132

Authors: Simona Svoboda

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