Young Kim: On implementing Euro-Bund futures

One of the exciting developments in finance over the last 25 years has been the growth of the derivatives markets. In many situations, both hedgers and speculators find it more attractive to trade a derivative on an asset than to trade the asset itself.

In this thesis, futures on bonds or so-called Cheapest-to-Deliver (CTD), are studied. Bond futures contracts are futures contracts that allow an investor to buy in the future a theoretical government notional bond at a given price at a specific date in a given quantity. Compared to other futures, bond futures are slightly more complicated as the underlying bond of the futures contract is not a physical bond but rather a theoretical notional bond determined by the basket of available deliverable government bonds issued in the market. At delivery of the futures contract, the holder will want to deliver the cheapest bond, hence bond futures are often called Cheapest-to-Deliver (CTD). The main objective of this thesis will be to, if possible develop a method to determine which bond will be the cheapest to deliver at the expiration of the future.

The term structure of the interest rates is assumed to be stochastic, and in particular the Ho-Lee model with a binomial short rate lattice is employed for the term structure modelling. Further, it is observed what effects changes in the terms structure have on which bond is the cheapest-to-deliver, since when interest rate changes it is natural to presume that another bond will become the cheapest-to-deliver.

The following questions will be discussed:

- How well does the Ho-Lee model fit the prices of bonds and futures?

- How many steps are needed in the binomial tree to get a good result?

- How do changes in the term structure affect which bond is the cheapest to deliver?

- Is it possible to predict which bond will be the cheapest to deliver?

- How sensitive is the futures price to changes in the zero curve?