In this post we will consider how the Black-Derman-Toy (BDT) short rate binomial tree will be used to price options on bonds.

Pricing Options

The BDT model may also be used to price put or call options on bonds. For the purpose of calculating these prices it is important to generate the entire short interest rate tree until the expiration of the option. The prices of the underlying coupon bearing instrument…

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In this post we will consider how the Black-Derman-Toy (BDT) short rate binomial tree will be used to price bonds.

Pricing Bonds

For example, we illustrate the use of the short rates to price a hypothetical 3-year fixed income bond at issue as follows:

Using the observed YTM and the excel price formula the price of the security works out to 99.94. Using the BDT model…

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Earlier we had looked at how the Black-Derman-Toy (BDT) interest rate model may be constructed in EXCEL. In particular we saw how the median rates and time varying volatilities (sigmas) of the short rate binomial tree were derived. In this post we will see how these values will be used to construct the complete short rate binomial tree.

Derivation of Short Rates

We have used the Black-Derman-Toy (BDT) interest rate model…

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Earlier we had considered how to define the various elements (input, output and calculation cells) of the Black-Derman-Toy (BDT) interest rate model in EXCEL. In this post we will link all these pieces together by using the Solver Function of the EXCEL worksheet. Once this has been done we will run the Solver Function to arrive at a solution for the median rates and their time varying volatilities (sigmas).

Define…

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In this post we continue with the definition of the calculation cells of the Black-Derman-Toy (BDT) model in EXCEL by seeing how yields are determined from the prices calculated from the state price lattices. We use these determined yields to derive the yield volatility of the lattice.

Define Calculation Cells d. Calculate Yields

 

As mentioned earlier the model is calibrated by equating the prices from the…

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Continuing with the definition of the calculation cells of the Black-Derman-Toy (BDT) model in EXCEL, we will see how prices are determined from the initial yield rates and from the three state price lattices in the post below.

Define Calculation Cells c. Calculate Prices from Lattice

Based on the lattices we now derive the prices as follows:

c.1.         Initial Price

This is simply the present value of a…

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In this post we continue with the definition of the calculation cells of the Black-Derman-Toy (BDT) model in EXCEL. Three state prices lattices are constructed.

Define Calculation Cells b. Construct State Price Lattices

The BDT model assumes that the short-term interest rates are log-normally distributed with risk-neutral probabilities of an interest rate going up or down in any time period of 0.5.

b.1.        State Price Lattice for deriving price at node 0

At node…

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Earlier we had defined the input and output cells for the Black-Derman-Toy (BDT) interest rate model. In this post we will consider how the first set of calculation cells, i.e. the short rate binomial tree will be defined in EXCEL.

Define Calculation Cells a. Construct short rate binomial tree

It is important to note here that in constructing the interest rate model these steps just set the stage and are not necessarily…

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