1 Bounds For Treasury Bond Futures Prices and Delivery Options Ren-Raw Chen and Shih-Kuo Yeh Comment by: San-Lin Chung Department of Finance, The Management School, National Central University, Chung-Li 320, Taiwan. Tel: , Fax: ,

2 Summary This paper derives the upper bound for the embedded options (including timing options and quality option) in T-bond futures. These upper bounds can be translated into a lower bound of T-bond futures price. The authors also show that the cost of carry model gives an upper bound of T-bond futures price. The numerical results show that these bounds are quite tight – about 2% higher or lower than the actual futures price.

3 Comments This paper is well written and contains a very interesting topic since T-bond futures is a very popular derivative. I have some suggestions which are hopefully helpful to the authors to improve their paper. 1.From figure 1, it seems that the true futures prices are some times close to the lower bounds, and some times close to the upper bounds. It might be interesting to investigate the possible reasons behind it.

4 2.Since the correlation between T-bond price and interest rate is negative, the T-bond forward price will be a upper bound of the T-bond futures price. The suggested upper bound will be tighter than the cost of carry model since the cost of carry model ignores the possibility that the cheapest to delivery bond may change in the future. 3.2% error may be a very tight bound for the option price (premium) but it is quite large to the futures prices. I wonder how these prices bounds can be implemented in trading?

5 4.It might be valuable to extend your data from 1991 to 2001 because the interest rates go down a lot during the recent years and it might affect the results.