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lynnguini · 2023年05月16日

这道题需不需要考虑accrued interest？

  1. CFA II
  2. Derivative

* 问题详情，请 查看题干

NO.PZ202108100100000105

问题如下：

Based on Exhibits 2 and 3, and assuming annual compounding, the per share value of Troubadour’s short position in the TSI forward contract three months after contract initiation is closest to:

选项：

A.

$1.6549.

B.

$5.1561.

C.

$6.6549.

解释：

C is correct.

The no-arbitrage price of the forward contract, three months after contract initiation, is

F0.25 = FV0.25(S0.25 + CC0.25 – CB0.25)

F0.25 = [$245 + 0 – $1.50 / (1 + 0.00325)(0.5-0,25) ] (1 + 0.00325)（0.75-0.25） = $243.8966.

herefore, from the perspective of the long, the value of the TSI forward contract is

V0.25= PV0.25 [F0.25 – F0]

V0.25= ($243.8966 – $250.562289)/(1 + 0.00325)（0.75-0.25） = –$6.6549.

Because Troubadour is short the TSI forward contract, the value of his position is a gain of $6.6549.

中文解析：

本题考察的是t时刻求value，有重新定价法和画图法两种方法。

上述求解过程为重新定价法，即先求t=3时刻的远期合约价格F，然后和F作差后折现至t时刻即可。

如果使用画图法，与课程讲法一致：假设是long position，向上箭头表收到，向下的箭头表支出，二者相减即为所求的value。对应本题需要注意的是short头寸，因此最后求得结果需要取负号即可。

具体计算过程如下图：

因为原题的设定，假如考虑了accrued interest，那AI_t和AI_T也会抵消；如果没有这么巧合的设定，这道题是不是需要考虑两个accrued interest？

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2 个答案

Lucky_品职助教 · 2023年05月19日

嗨，努力学习的PZer你好：


accrued interest定义如下，因此AI_t是截止到t时刻的AI，AI_T是截止到T时刻的AI

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就算太阳没有迎着我们而来，我们正在朝着它而去，加油！

Lucky_品职助教 · 2023年05月17日

嗨，爱思考的PZer你好：


是的，如果考虑了accrued interest，则需要考虑两个accrued interest。具体来说，在计算远期合约价格F时，应将CB0.25和CC0.25中的当前时间（t=0）的accrued interest加入到对应的价格中。

在计算V0.25时，还需要加上t=0时刻到t时刻的accrued interest AI_t和t=0时刻到T时刻的accrued interest AI_T，即：

V0.25 = [F0.25 - F0] / (1 + r)^(T-t) - AI_t - AI_T

因此，在考虑accrued interest的情况下，对于本题的求解需要进行相应的调整。

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就算太阳没有迎着我们而来，我们正在朝着它而去，加油！

lynnguini · 2023年05月18日

Rf不变的情况下，这两个accrued interest不是相等吗？

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