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?