# Black Derman Toy (BDT) Interest Rate Model – Topic Guide

 Interest Rate Models are used to value various financial instruments. The models are defined by state variables and their processes. The values taken by the state variables represent the position or state of the item being model. The processes determine how the state variables change over time and may depend on the evolution of a single factor or multiple factors. The Black-Derman-Toy interest rate model is an example of the former.

The Black-Derman-Toy term structure model was developed by Fischer Black, Emmanuel Derman and William Toy in 1990. It is an example of a No-Arbitrage model. It assumes that all security prices and rates depend on only one single factor- the short rate.

### Topics covered:

1. An overview of the basic features of a Black-Derman-Toy (BDT) one factor interest rate model as well as some of the simplifying assumptions made in its construction.
2. A step-by-step methodology demonstrating how the Black-Derman-Toy (BDT) one factor interest rate model may be built in EXCEL. This includes:
• A definition of the input , output and calculation cells
• Linking all the pieces together with the Solver Function of the EXCEL worksheet and running the Solver Function to get the results, i.e. median rates and their time varying volatilities (sigmas).
3. The construction of a short rate binomial tree from the median rates and volatilities determined.
4. Illustrate, using an EXCEL worksheet, how the rates from this tree will be used to price bonds and options.

### EXCEL files

The pre-packaged course deal also includes the following 2 EXCEL files that demonstrate the following concepts:

1. How to build a BDT interest rate model in excel
2. How to utilize the results of the model to price bonds and options

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