In finance, the Black-Derman-Toy model is a model of the evolution of the yield curve, sometimes referred to as a short rate model. It is a one-factor model; that is, a single stochastic factor (the short rate) determines the future evolution of all interest rates. One can calibrate the parameters in the BDT model to fit the current term structure of interest rates (yield curve) as well as volatility structure as derived from implied (from the Black-76 model) prices for interest rate caps. From here, one can value a variety of more complex interest-rate sensitive securities.

The model was introduced by Fischer Black, Emanuel Derman, and Bill Toy. It was first developed for in-house use by Goldman Sachs in the 1980s and was eventually published in the Financial Analysts Journal in 1990. A personal account of the development of the model is provided in one of the chapters in Emanuel Derman's memoir "My Life as a Quant."

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