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erin_hi1990 · 2023年06月13日

ai应该算在哪个FV中？

  1. CFA II
  2. 其他
  3. Derivative

NO.PZ2023041003000016

问题如下：

Troubadour identifies an arbitrage opportunity relating to a fixed-income futures contract and its underlying bond. Current data on the futures contract and underlying bond are presented in Exhibit 1. The current annual compounded risk-free rate is 0.30%.


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：

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

F0(T) =FV0,T(T)[B0(T + Y) +Al0– PVCI0,T]

F0(T)= (1 + 0.003)0.25(112.00 + 0.08 - 0)

F0(T) = (1 + 0.003)0.25 (112.08) = 112.1640

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

F0(T)=CF(T)QF0(T)

F0(T) = (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.

请问accrued interest at futures contract expiration0.2 为什么要算进期货合约的value里而不是在现货fv中扣减掉？谢谢

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1 个答案

Lucky_品职助教 · 2023年06月14日

嗨，努力学习的PZer你好：


accrued interest是指已经产生但尚未支付的利息，它是利息应计的一部分，此时债券发行人已经占用了投资者的资金，因此投资者有资格要求偿还这部分利息。在这道题目中，我们需要在期货合约价值中加入到期时的应计利息，因为在到期时，如果有人持有这个期货合约，则合约的买方需要支付给卖方该债券的全部价值及其中应计的利息作为剩余盈利的补偿。

而在现货的FV中，已经考虑了应计利息。因此，我们对于现货部分的价值计算使用了当前债券价格，即112.00。而对于期货部分的价值计算，我们需要加上应计利息0.20，得到总价值为112.70。这样计算可以更准确地反映出期货市场的实际交易情况，因此应计利息需要计入期货合约的价值中。

因此，accrued interest at futures contract expiration0.2 在计算期货合约的价值时需要加上，而在现货的FV中则已经被考虑了。

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