## Determining the Cheapest-to-Deliver Bonds for Bond Futures

##### Summary

In this research futures on bonds are studied and since this future has several bonds as its underlyings,
the party with the short position may decide which bond it delivers at maturity of the
future. It obviously wants to give the bond that is the Cheapest-To-Deliver (CTD). The purpose
of this project is to develop a method to determine, which bond is the CTD at expiration of
the future. To be able to compare the underlying bonds, with different maturities and coupon
rates, conversion factors are used.
We would like to model the effects that changes in the term structure have on which bond is
cheapest-to-deliver, because when interest rates change, another bond could become the CTD.
We assume that the term structure of the interest rates is stochastic and look at the Ho-Lee
model, that uses binomial lattices for the short rates. The volatility of the model is supposed
to be constant between today and delivery, and between delivery and maturity of the bonds.
The following questions will be analysed:
• Is the Ho-Lee model a good model to price bonds and futures, i.e. how well does the model
fit their prices?
• How many steps are needed in the binomial tree to get good results?
• At what difference in the term structure is there a change in which bond is the cheapest?
• Is it possible to predict beforehand which bond will be the CTD?
• How sensitive is the futures price for changes in the zero curve?
• How stable are the volatilities of the model and how sensitive is the futures price for
changes in these parameters?
To answer these questions, the German Euro-Bunds are studied, which are the underlying bonds
of the Euro-Bund Future.