Both the Vasicek and CIR models, as discussed in Chapters 1 and 2, incorporate a deterministically mean reverting process. In these models, the mean reversion is incorporated without additional assumptions about the future behaviour of the short-term interest rate volatility. This is a highly desirable feature. By allowing time-dependent parameters and therefore the matching of any arbitrary initial yield curve, HW manage to overcome one of the major drawbacks of the Vasicek and CIR models. The HW-extended Vasicek model is usually implemented with constant absolute volatility and reversion speed. However, in some yield curve environments, such as rising term structure of rates and declining term structure of volatilities, this version of the model provides a rather poor fit to observed cap prices [ 45 ]. On the other hand, allowing time-dependent absolute volatility and reversion speed results in unsuitable behaviour of short-term interest rate volatilities in the future. If these shortcomings are recognised and accounted for during the calibration process, the extended Vasicek model can be of great value, since it allows for closed-form solutions of discount bond and discount bond option prices.