Interest Rate Modelling the case of one-factor CIR term structure model - kamboj, navjot (2009)
We emphasise on one of the first general equilibrium single-factor Cox-Ingersoll-Ross (1985b) term structure model. Using weekly quotes for the period 1962-2006 of 3-Year constant maturity U.S. treasury bills, we investigate the robustness of the CIR model in depicting the evolution of interest rates. Due to high volatility during the era of 1979-1982, the data is sub divided into three time frames. The econometric approach used for maximizing the model parameters is the Maximum-likelihood estimation, pioneered by Irvin Fisher. Further we use Monte-Carlo simulation for probable distribution of interest rates in the time horizon. Our findings conclude with the failure of the CIR model in times of high volatility in interest rates. Further research can be undertaken with special emphasis on the volatility factor of interest rate models. However our conclusion is limited to single-factor CIR model, hence there can be more significant or precise single or multi-factor models that can describe the dynamics of interest rate volatility in a robust manner. Moreover due importance should be given on data selection for any model, as high oscillations in the data set can lead to significant effects in term structure modelling. Another aspect to be emphasised on during term structure modelling, is the econometric approach being used for evaluating the model parameters. It needs to be seen as to what assumptions and features of different econometric approaches are supported by the interest rate model being considered.