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94逢考必过 · 2024年10月26日

请问这道题的AIt是30么

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.

请问这道题的AIt是30么

1 个答案

李坏_品职助教 · 2024年10月26日

嗨,爱思考的PZer你好:


题目解析中的29.778 * 1.015这个不是AI,这个是FVCI。


本题是计算price of the forward contract,也就是计算FP,不需要减去AI。减去的29.778 * 1.015这个是FVCI,也就是forward存续期内两笔coupon的终值。


本题的条件不足,不知道从上一次支付coupon到现在具体过了多长时间,所以也无法求出AIT。

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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!

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