Abstract
For an interest rate model to predict future rates, it is highly desirable that it has embedded in it the current term structure of interest rates known in the market. For the general four-parameter interest rates model incorporating the current yield into the model seems intractable. In the present paper we consider a first order approximation, valid for large time to maturity, to fit the current yield curve into the model. The resulting interest rate model is described which includes, as a particular case, the well-known interest rate model of Vasicek (11).
Highlights
The first short rate model to be proposed was by Vasicek [11]: dr = a (b − r) dt + σdX
For an interest rate model to provide future rates, it is highly desirable that it has embedded in it the current term structure of interest rates known in the market
We refer to the resulting interest rate model as FourParameter Interest Rate Model (FP-IRM)
Summary
The first short rate model to be proposed was by Vasicek [11]: dr = a (b − r) dt + σdX. To overcome the possibility of interest rates becoming negative in the Vasicek model, Cox, Ingersoll and Ross [4] proposed the short rate model:. To incorporate a pre-assigned term structure of interest rates, short rate models have been considered with time dependent parameters. In the present paper we consider a first order approximation, valid for large time to maturity, to fit the current term structure of interest rates into the model. The resulting interest rate model is described which includes, as a particular case, the well-known interest rate model of Vasicek [11]
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