# How to construct a Black Derman Toy Model in EXCEL

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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.

This course presents a step-by-step methodology write-up of how to build a one factor interest rate model in EXCEL. This includes:

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 guide demonstrating how the Black-Derman-Toy (BDT) one factor interest rate model may be built in EXCEL. This includes:
• Defining the input cells (including the initial zero yield curve & volatility term structures)
• Defining the calculation cells (including the state price lattices, short rate tree, prices, yields and yield volatilities)
• Defining the output cells (including mediate rates and volatilities)
• Linking all the pieces together with the Solver Function of the EXCEL worksheet
• Running the Solver Function to get the results, i.e. median rates and their time varying volatilities (sigmas)

(Note: EXCEL file is not included)

Learning Objectives

After taking this course you will be able to:

• Describe the basic features of the BDT interest rate model
• List the simplifying assumptions used in the construction of the model
• Build a BDT model in EXCEL
• Derive results for the model, i.e. the median rates and time varying volatilities by setting and running the Solver functionality in EXCEL

Prerequisites

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

Target Audience

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

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