Calibration of different interest rate models for a good fit of yield curves

One of the first mathematical models to describe the interest rate over time was the Vasicek model (1978). Soon after, the Cox Ingersoll Ross (CIR) model (1985) was introduced. The Vasicek model and the CIR model belong to the family of short interest rate models. Through transformation these models can be applied to compute the interest rate values. Classical techniques such as the Maximum Likelihood Estimate (MLE) and Least Squares Method (LSM) are used to estimate the parameters in the short rate model from the historical data. One must understand that the short rate values cannot be observed from the financial market. However, we can observe the bond prices and from these we can compute the interest rates values. It turns out that when the short interest rate values are not known, MLE and LSM cannot be used to estimate the parameters in the CIR model. Rabobank encountered this problem. My assignment was to estimate the parameters in the CIR model using the historical data collected by Rabobank. When doing calibration using MLE or LSM for the Vasicek model, it turns out that the drift parameters are estimated with very high bias. Rabobank uses the Long Term Quantile (LTQ) method, which is expected to have no bias. My assignment was to test this claim and see whether there is a bias and if so I had to eliminate this bias.FinanceApplied mathematicsElectrical Engineering, Mathematics and Computer Scienc