Black-Derman-Toy model

Other models that are similar in concept are the Black-Derman-Toy (1990) and Black-Karinski (1992) models, however these have different terms for the drift rate and require numerical fitting to the initial interest rate and volatility term structures. The drift rate term is not known analytically in these models. In the BDT model the short-term rate volatility is related to the strength of the mean reversion in a way that reduces the volatility over time. 

Incorrect calibration produces errors in option valuation that may be discovered only after significant losses have been suffered. If the necessary data are not available to calibrate a sophisticated model, a simpler one may need to be used. This is not an issue for products priced in major currencies such as the dollar, sterling, or euro, but it can be a problem for other currencies. That might be why the B-S model is still widely used today, although models such as the Black-Derman-Toy and the one proposed in Brace, Gatarek, and Musiela (1994) are increasingly employed for more exotic option products. 

In the models we have reviewed in this chapter, there has only been (me function of time, the parameter a. In certain models, either or both of the parameters a and a are also made to be functions of time. In their 1990 paper Black, Derman and Toy (BDT) proposed a binomial lattice model described by Equation (3.60),... 

Black, F., Derman, E., Toy, W., 1990. A one-factor model of interest rates and its application to Treasury bond options. Financ. Anal. J. 46, 33-39. 

Black, E, E. Derman, and W. Toy. 1990. A One-Factor Model of Interest Rates and Its Application to Treasury Bond Options. Einancial Analysts Journal, Spring, 33-39. 

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