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# Calibration of Black Derman Toy (BDT) Interest Rate model to US Treasuries

**About the course**

This course consists of two EXCEL files that illustrate the calibration of the 5-year semi-annual Black Derman Toy (BDT) interest rate model as at a given valuation date using two different methodologies:

- Under the first methodology the model’s outputs, median rates and sigmas, are determined by calibrating the model so that
- Prices from the price lattices of the model = Prices derived using the initial zero curve yield rates
- Volatilities from the prices lattices of the model = initial volatility term structure

*Note: The initial zero curve yield rates and initial volatility term structure are assumed to have already been derived from the US Treasury yield curve data, are considered inputs into the model and are not calculated in this file but are taken as given.*

The resulting short rates tree is used to price US Treasuries to see the fit of the model, i.e. the extent of the difference between actual and model prices as at the valuation date.

The second alternate methodology reduces the difference between the actual and model prices as at the valuation date so that the model is more truly marked to market. In this instance, the outputs, median rates and sigmas, are determined by calibrating the model so that

- Prices from the price lattices of the model = Prices derived using the initial zero curve yield rates
- Differences between modelled and observed US Treasury bond prices are reduced

For this model, volatilities from the price lattices of the models are not set equal to the initial volatility inputs.

By its very construction and calibration, using the resulting short rate tree to price US Treasury bonds will produce prices that will match the observed prices as at the valuation date. Hence, the latter model will produce results that exactly marked to market.

**Learning Objectives**

After taking this course you will be able to:

- Construct a BDT model in EXCEL
- Calibrate the model to prices and the initial volatility term structure
- Price bonds using the outputs of the BDT model
- Calibrate the model to prices and minimize the difference between computed and observed bond prices

**Prerequisites**

Familiarity with basic mathematics, probability, statistics and EXCEL. Some knowledge of bond and derivative markets including how to derive zero coupon rates and volatilities from yield curve rates.

**Target Audience**

The course is aimed at individuals responsible for asset liability management and risk management, including the simulation and stress testing of rate sensitive asset and liability portfolios within banks, insurance companies, mutual funds as well as those involved in the pricing of money market, derivatives and structured products.