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Ryoooh · 2020年03月15日

问一道题:NO.PZ2020021204000036 [ FRM I ]

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).

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

对于各个名词(quored price VS clean future price VS quoted future price)有点混淆,如何知道最后要不要除CF呢?是因为最后计算出来的只是delivered bond的clean future price,所以要还原成标准债券(半年计息,票面息率6%)的quoted future price对吧?
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已采纳答案

袁园_品职助教 · 2020年03月15日

同学你好!

是的。

clean/quoted price + AI = dirty price

这道题是已经告诉你CDT bond 的信息让你反求 quoted future price,基本原理就是我以现在的价格short 这个债券获得一笔钱(这笔钱是要包含 AI的,因为是实际交易价格),一个月后要把债券从市场上买过来还给别人。

所以先得到 dirty price,向后复息一个月,这个价格就是 quote future price * CF + AI

可以再去听一下讲课的视频,尝试自己总结一下,加油!

 

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