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胖胖 · 2023年10月10日

accrued interest

  1. CFA II
  2. Derivative

NO.PZ2019010402000058

问题如下：

Eden wants to purchase a 15-year Treasury note futures contract. The underlying 3%, semi-annual Treasury note has a dirty price of 105. It has been 60 days since the last coupon payment. The futures contract expires in 90 days. The current annualized three-month risk-free rate is 1.60%. The conversion factor is 0.80. the equilibrium quoted futures contract price based on the carry arbitrage model is:

选项：

A.

103.1665

B.

104.1675

C.

130.2094

解释：

C is correct。

画图法解析如下：


注意：

1. 计算AIT 时对应的时间是150天。

站在0时刻距离上一次票息日是60天，然后合约是接下来的90天，所以在T时刻对应的AI是150天的。

2. 本题求解的是Q0 ，即上图中右下角的结果是130.2094，不是求解的F0。

accrued interest should be 60/180X coupon of $1.5.


Because it is days from last coupon payment, that's 60 days.

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1 个答案

pzqa35 · 2023年10月10日

嗨，努力学习的PZer你好：


From the question, we can see that the last coupon payment is 60 days away from the current time point, which is time 0. However, the maturity date of this futures is 90 days, and the entire bond coupon is paid every six months. Therefore, there is a total of 150 days from the last coupon payment to the maturity of the futures, which means that the cumulative time for AIT is 150 days. So AIT=(150/180) * (3% * 100/2)=1.25.

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