The Black and Karasinski Model

The discrete time Black, Derman and Toy model [6], discussed in Chapter 8, makes provision for two time-dependent factors: the mean short-term interest rate and the short-term interest rate volatility. The continuous time equivalent of the model clearly shows that the rate of mean reversion is a function of the volatility. This is equivalent to future short-term interest rate volatilities being fully determined by the observed volatility term structure. This dependence makes it impossible to specify these two factors independently.