Embedded options and hedging with bund futures

In this study we adopt a methodology based on the model in Heath. Jarrow and Morton (1992) for pricing and analyzing the Bund Futures Contract and its embedded options assuming a stochastic term structure of interest rates. The HJM model which utilizes the information implied in observable discount (zero coupon) bond prices can obtain an arbitrage-free valuation for interest rate contingent claims in a risk-neutral world. The only required inputs for this model are the term structure of interest rates and its volatility function. Unfortunately. the pure discount bond price is not always directly observable from the market. It needs to be estimated from observable coupon bond prices by an appropriate technique. In this study. we use the B-Spline approximation adopted by Steeley (1991) to estimate the term structure of interest rates. Due to the complexity of the bond futures contract which involves several deliverable coupon bonds each of which is a portfolio of a number of pure discount bonds. a closed -form valuation formula is very difficult to obtain. We construct a binomial apprOximate model to evaluate the bond futures contract and its embedded options. in particular. the conventional quality option and the new-issue quality option. The binomial model is very flexible and it can also be applied to evaluate a wide range of various interest rate derivative securities. With the assumption of a constant volatility for each forward interest rate over time. the binomial model is path-independent saving lots of time in calculation. With our methodology, we can also value options on bond futures contracts. We try to utilize the information implied in call options on bund futures for estimating the term structure volatility. Although it is inconclusive, this methodology can be applied for studying the pricing of other bond futures contracts and their embedded options. Since hedging is the primary purpose of a futures contract. we also discuss strategies to hedge cash bond positions with bond futures contracts. In the content of our methodology, we can construct a dynamic hedging strategy for hedging bond price changes due to interest rate risks. We also explore the role of the delivery option in hedging effectiveness. and conclude that there is no evidence that the delivery option harms the hedging effectiveness of bond futures contracts.