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xiaobaiybz · 2022年04月20日

老师,这道题我这么做对么?感觉跟答案不太一样呢?

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NO.PZ202108100100000101

问题如下:

Based on Exhibit 1 and assuming annual compounding, the arbitrage profit on the bond futures contract is closest to:

选项:

A.

0.4158.

B.

0.5356

C.

0.6195

解释:

B is correct.

The no-arbitrage futures price is equal to the following:

F0 = FV[B0 + AI0 – PVCI]

F0 = (1 + 0.003)0.25(112.00 + 0.08 – 0) = 112.1640.

The adjusted price of the futures contract is equal to the conversion factor multiplied by the quoted futures price:

F0 = CF × Q0

F0 = (0.90)(125) = 112.50

Adding the accrued interest of 0.20 in three months (futures contract expiration) to the adjusted price of the futures contract gives a total price of 112.70.

This difference means that the futures contract is overpriced by 112.70 – 112.1640 = 0.5360. The available arbitrage profit is the present value of this difference: 0.5360/(1.003)0.25 = 0.5356.

中文解析:

本题考察的是长期国债期货的套利过程。

关于长期期货合约,注意Q0作为报价但不是成交的报价,F0 是成交的报价。

本题中,首先我们需要判断市场上的长期国债期货合约的报价是否合理。

根据公式F0 = FV[B0 + AI0 – PVCI] 计算出合理的报价为112.1640;而此时市场上期货合约可以成交的报价为F0 = CF × Q0 =112.50;

显然市场上的期货合约定价过高了,因此如果执行套利操作,需要short futures,对应的应该long 现货。

于是在T时刻,我们的套利空间为[F0 +AIT] - [(S0 +AI0 )(1+rf)T]=112.50+0.20 -112.1640=0.5360;

折现至0时刻,则套利产生的profit= 0.5360/(1.003)0.25 = 0.5356.


老师,这道题我这么做对么?感觉跟答案不太一样呢?


1 个答案

Lucky_品职助教 · 2022年04月23日

嗨,从没放弃的小努力你好:


同学你做的对呀,我计算出结果是一样的,答案是先在3时刻相减,再折现到0时刻,你是先折现到0时刻,再想减,殊途同归哦~

----------------------------------------------
加油吧,让我们一起遇见更好的自己!

Darlene · 2024年07月03日

老师,我按上面同学的画图的做出来,答案也不对啊?

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