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SHAO · 2024年07月17日

老师，没看懂答案，这个题maturity不是7年吗？能用画图法讲解一下吗

  1. CFA II
  2. Derivative

NO.PZ2023020101000010

问题如下：

Three months ago (90 days), Kim purchased a bond with a 3% annual coupon and a maturity date of seven years from the date of purchase. The bond has a face value of US$1,000 and pays interest every 180 days from the date of issue. Kim is concerned about a potential increase in interest rates over the next year and has approached Riley for advice on how to use forward contracts to manage this risk. Riley advises Kim to enter into a short position in a fixed-income forward contract expiring in 360 days. The annualized risk-free rate now is 1.5% per year and the price of the bond with accrued interest is US$1,103.45.

Based on a 360-day year, the price of the forward contract on the bond purchased by Kim is closest to：

选项：

A.

US$1,082.

B.

US$1,090.

C.

US$1,120.

解释：

Note that time 0 is the forward contract initiation date, that is, 90 days after the purchase of the bond. Time T is the contract expiration date, that is, 360 days.

The forward contract price follows:

F0(T) = FV0,T [S0 – PVCI0,T]

Present value (PV) of coupons = PVCI0,T = 15/(1.015)90/360 + 15/(1.015)270/360 = 14.944 + 14.833 = US$29.778

F0(T) = (1103.45 – 29.778)(1.015)360/360 = US$1,090.

协会教材在这里写的有矛盾，参见下面两个公式，一个是需要调整AIT，但是另一个又不需要进行调整。



根据它的题目来看就是如果是根据标的资产的价格去求FP，那就不要减去AIT，但是如果要求QFP，就还需要减去AIT之后做转换.

老师，没看懂答案，这个题maturity不是7年吗？能用画图法讲解一下吗

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3 个答案

pzqa35 · 2024年08月26日

嗨，从没放弃的小努力你好：


这里是乘以，乘号被省略了，求定价是要乘以(1+rf)^T哈。

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就算太阳没有迎着我们而来，我们正在朝着它而去，加油！

pzqa35 · 2024年07月19日

嗨，从没放弃的小努力你好：


这里是乘法哈，没写出来，这个就是FP的计算公式:FP=(S0-PVC0)*(1+rf)^T


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虽然现在很辛苦，但努力过的感觉真的很好，加油！

Emma0627 · 2024年08月24日

这里是不是应该T270/360，毕竟1年的contract不是270天要到期了吗？

pzqa35 · 2024年07月18日

嗨，努力学习的PZer你好：


Riley advises Kim to enter into a short position in a fixed-income forward contract expiring in 360 days. 7年是债券的到期日，forward是1年到期的。这里是求forward的定价。


Present value (PV) of coupons =15/(1.015)^90/360 + 15/(1.015)^270/360 = 14.944 + 14.833 = US$29.778

F0(T) = (1103.45 – 29.778)(1.015) = US$1,090.

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就算太阳没有迎着我们而来，我们正在朝着它而去，加油！

SHAO · 2024年07月18日

老师，最后一步F0(T) = (1103.45 – 29.778)(1.015) = US$1,090.为啥又除一个1.015呢？1103.45和coupon不都是0时刻的吗

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