Prediction of Interest Rate using CKLS Model with Stochastic Parameters

The Chan, Karolyi, Longstaff and Sanders (CKLS) model is a popular one-factor model for describing the spot interest rates. In this paper, the four parameters in the CKLS model are regarded as stochastic. The parameter vector phi((j)) of four parameters at the (j+n)-th time point is estimated by the j-th window which is defined as the set consisting of the observed interest rates at the j'-th time point where j <= j' <= + n. To model the variation of phi((j)), we assume that phi((j)) depends on phi((j-m),) phi((j-m+1)),..., phi((j-1)) and the interest rate r(j+n) at the (j+n)-th time point via a four-dimensional conditional distribution which is derived from a [4(m+1)+1]-dimensional power-normal distribution. Treating the (j+n)-th time point as the present time point, we find a prediction interval for the future value r(j+n+1) of the interest rate at the next time point when the value r(j+n) of the interest rate is given. From the above four-dimensional conditional distribution, we also find a prediction interval for the future interest rate r(j+n+d) at the next d-th (d >= 2) time point. The prediction intervals based on the CKLS model with stochastic parameters are found to have better ability of covering the observed future interest rates when compared with those based on the model with fixed parameters.