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Sibyl · 2023年10月01日

能不能用画图大法解释下呢？

  1. CFA II
  2. Derivative

NO.PZ2023020101000010

问题如下：

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

Based on a 360-day year, the price of theforward 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：

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

Theforward contract price follows:

F0(T)= FV0,T [S0 – PVCI0,T]

Presentvalue (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.

如题，后面提问的答案看起来也是晕的。

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3 个答案

pzqa35 · 2024年01月29日

嗨，爱思考的PZer你好：


题目中有说到Three months ago (90 days), Kim purchaseda bond with a 3% annual coupon and a maturity date of seven years from the dateof purchase，也就是说这个资产是90天之前买的，每180天付息一次，所以在0时刻而言，90天之后就会付利息了。这个题比较绕的一点就是这个投资者不是在买标的资产的同时就签定forward，而是过了90天以后才签定的，因此站在0时刻来看的话付息的时间点是就是会提前一些。

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虽然现在很辛苦，但努力过的感觉真的很好，加油！

pzqa35 · 2023年10月06日

嗨，从没放弃的小努力你好：


这个债券的是从0时刻开始，每180天付一次利息，但是现在已经过了90天我才进入了forward contract，但是债券付息的时间不会因为我买入forward的时间而改变，还是到了180天会付息，也就是买入forward的90天后就会有第一笔coupon。

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加油吧，让我们一起遇见更好的自己！

pzqa35 · 2023年10月04日

嗨，努力学习的PZer你好：


本题考察的是对fixed-income forward定价。

我们把签订远期合约的时刻定为0时刻，需要对一年期的远期合约进行定价。

关于标的债券的已知条件：当前的价格S0=$1,103.45；每半年（180天）支付一次票息，金额为3%*$1,000*1/2=$15；距离上一次支付票息已经过去了90天。因此在接下来的一年里有两笔票息的支付，分别发生在90天以后，270天以后。

因此根据远期合约的定价公式F0(T) = FV0,T [S0 – PVCI0,T]，该远期合约的价格.

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.

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努力的时光都是限量版，加油！

Sibyl · 2023年10月05日

a maturity date of seven years from the dateof purchase 不应该是90天前开始算，那么应该第一个coupon应该是购买日到180天吧？

啦啦啦啦啦 · 2024年01月28日

；距离上一次支付票息已经过去了90天。 老师您好，请问这个是怎么看出来的呀？

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