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Sibyl · 2023年10月04日

能不能用直接套用公式算一次？

  1. CFA II
  2. Derivative

NO.PZ2023020101000011

问题如下：

They move to valuation of a bond futures contract employed by Sheroda. Parisi provides Curry with the following information for a Treasury bond and calculates the price of a futures contract on this bond. The bond has a face value of $100,000, pays a 7% semiannual coupon, and matures in 15 years. The bond is priced at $156,000, has no accrued interest, and yields 2.5%. The futures contract expires in 8 months, and the annualized risk-free rate is 1.5%. There are multiple deliverable bonds, and the conversion factor for this bond is 1.098.

Based on the information provided by Parisi, which of the following correctly calculates the futures price of the Treasury bond：

选项：

A.

f 0 ( T )= [ $156,000 ( 1.015 ) ( 8/ 12 ) −$3,508.6958 ] /1.098 =$140,298.21.

B.

f 0 ( T )= [ $156,000 ( 1.015 ) ( 8/ 12 ) −3,491.325 ]/ 1.098 =$140,314.03.

C.

f 0 ( T )=1.098[ $156,000 ( 1.015 ) ( 8/ 12 ) −$3,508.6958 ]=$169,144.08.

解释：

The futures price is calculated as follows:

f 0 ( T )= 1 /CF( T ) { FV[ B 0 ( T+Y )+A I 0 ]−A I T −FVC I 0,T }

There is no accrued interest, but the bond pays a $3,500 coupon in 6 months, so the future value of the coupon at expiration will be $3,508.6958 = 3500(1.015)(2/12).

f 0 ( T )= [ $156,000 ( 1.015 ) ( 8/ 12 ) −$3,508.6958 ] /1.098 =$140,298.21.


就这个解析里，老师说可以直接套用公式，我自己套了下，有点儿晕了😳



就下面直接用公式我带入就晕了……

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1 个答案

pzqa35 · 2023年10月06日

嗨，爱思考的PZer你好：


本题考察的是对fixed-income futures估值。

注意这道题目出的不是很严谨，解析中也有一些错误。关于本题，重点回顾对fixed-income futures定价的知识点，对答案和解析不必纠结。

首先，看一下选项中给的都是f0(T),但是具体的表达式中涉及到除以CF（1.098），因此可以推断题目本身要问的是QFP。

然后，根据题干信息可知：标的债券面值为$100,000，票息率为7%，半年付息一次，15年到期。并且告诉我们B0=$156,000，无风险利率为1.5%，合约还有8个月到期，CF为1.098。没有accrued interest。

具体分析：没有accrued interest，即AI0=0；半年付息一次，因此6个月的时刻会有一笔coupon。根据画图法可知，在0时刻：

向上的箭头为：B0+AI0-PVC=$156,000 + 0 – [$100,000*7%*1/2] / (1+1.5%)6/12;

向下的箭头为：FP+AIT向前折现8个月到0时刻的值，即QFP*CF+AIT向前折现8个月的值，具体为：[QFP*1.098+AIT] / (1+1.5%)8/12 ;

令向上箭头等于向下的箭头，可得：

选项A中忽略了AIT (即上面式子中分母位置的100,000*7%*1/2*2/6)，因此选项A虽然是本题的答案，但是也是有些许问题的。

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虽然现在很辛苦，但努力过的感觉真的很好，加油！

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NO.PZ2023020101000011 问题如下 They move to valuation of a bonfuturescontraemployeShero. Parisi provis Curry with the followinginformation for a Treasury bonancalculates the priof a futures contraonthis bon The bonha favalue of $100,000, pays a 7% semiannucoupon,anmatures in 15 years. The bonis price$156,000, hno accruenterest, anyiel 2.5%. The futures contraexpires in 8 months, antheannualizerisk-free rate is 1.5%. There are multiple liverable bon, antheconversion factor for this bonis 1.098.Baseon the information provibyParisi, whiof the following correctly calculates the futures priof theTreasury bon A.f 0 ( T)= [ $156,000 ( 1.015 ) ( 8/ 12 ) −$3,508.6958 ] /1.098 =$140,298.21. B.f 0 ( T )= [ $156,000 ( 1.015 )( 8/ 12 ) −3,491.325]/ 1.098 =$140,314.03. C.f 0 ( T )=1.098[ $156,000 (1.015 ) ( 8/ 12 ) −$3,508.6958]=$169,144.08. Thefutures priis calculatefollows:f 0 ( T )= 1 /CF( T ) { FV[ B 0 ( T+Y )+A I 0]−A I T −FVC I 0,T } Thereis no accrueinterest, but the bonpays a $3,500 coupon in 6 months, so thefuture value of the coupon expiration will $3,508.6958 = 3500(1.015)(2/12).f 0 ( T )= [ $156,000 ( 1.015 ) ( 8/ 12 ) −$3,508.6958 ] /1.098 =$140,298.21.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，这道题为什么是2/12么？为什么它这个FP期权签约的时候是t=0，不是其他月份呢？ 例如3月签FP，债券是半年发一次，6时发copon，11月FP到期，那就不是2/12？ 我理解这道题求的FP，那为什么是乘以1/CF呢？

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