问题如下:
Assume that the bond that will be cheapest to deliver in a Treasury bond futures contract pays semi-annual coupons at the rate of 10% per annum on May 1 and November 1 and will be delivered on September 1. The bond's quoted price on August 1 is 130.00 and its conversion factor is 1.2341. Estimate the futures price on August 1 assuming that all interest rates are 4% (continuously compounded).
选项:
解释:
There are 92 days between May 1 and August 1 (30, 30,31, and 1 in May, June, July, and August, respectively) and 184 days between May 1 and November 1 (30, 30, 31, 31, 30, 31, 1 in May, June, July, August, September, October, and November, respectively). The dirty price of the bond is therefore:
130 + 5 X 92/184 = 132.5
No coupons will be paid in the 31-day period between August 1 and September 1. The time to delivery is 31/365 = 0.0849 years. The dirty futures price is therefore:
132.5e0.0849X0.04=132.9509
The accrued interest on September 1 is 5 X 123/184= 3.3423. The clean futures price is therefore:
132.9509 - 3.3423 = 129.6086
Dividing by the conversion factor we obtain the estimated futures price as:
129.6086/1.2341= 105.0227
老师求顺一下逻辑:short 方先前已经short了bond futures,拿到QFP*CF+AIT的钱,现在市场上有个亿CDT130应该是B0,B0+31天的利息得到full price,因为实际是在T时间交割,那么full price滚到sep1 号,得到当天的真实的购买成本,扣掉AIT,乘以1/CF,得到的就是当时(最早的时候)我short 的那个bond future 的clean price。bond future price应该就是最早先前short bond future的那个报价吧?