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Ryoooh · 2020年10月10日

问一道题:NO.PZ2016082402000060

问题如下:

The yield curve is upward sloping. You have a short T-bond futures position. The following bonds are eligible for delivery:

The futures price is 103-17/32 and the maturity date of the contract is September 1. The bonds pay their coupon semiannually on June 30 and December 31. The cheapest to deliver bond is:

选项:

A.

Bond A

B.

Bond C

C.

Bond B

D.

Insufficient information

解释:

ANSWER: B

The cost of delivering each bond is the price divided by the conversion factor. This gives, respectively, (102+14/32)/0.98 = 104.53, 103.49, and 103.34. Hence the CTD is bond C. All other information is superfluous.

Or we can use the complete method: cost= Bond price - Future price* conversion factor, and we can find choice B is the answer.

看了之前同学的提问,追加问一下AI 相关的问题。


老师在另一个解答里说:

"在求最便宜交割债券时,AI是可以约掉、不用考虑的。因为short方在T时刻收到的钱是FP*CF + AI,然后short方挑选一个最便宜的债券给long方,这个最便宜的债券的价格是SP + AI,这个相当于是short方的成本。所以short方的收益时 FP*CF - SP。要挑选最便宜交割债券,即最大化这个收益。而这个收益表达式中不含AI。"


但是我理解是最便宜的债券和标的债券的AI 是不一样的,比方CTD的债券是100 16/32, 我的标的债券是101 1/32, 分别两个债券的AI 会有微小差别。这里是因为差距太小直接约掉了还是说AI都是算标的债券的AI呢?

1 个答案

小刘_品职助教 · 2020年10月10日

同学你好,

转换因子CF在计算的时候本身已经考虑了交割债券票面利率和国债期货模拟票面利率之间的差异,所以不需要额外再考虑AI。

以我国的5年国债期货为例,CF公式如下

其中,r:5年期国债期货合约票面利率3%;

x:交割月到下一付息月的月份数;

n:剩余付息次数;

c:可交割国债的票面利率;

f:可交割国债每年的付息次数。

计算结果四舍五入至小数点后4位。

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