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Kiki · 2024年05月03日

现金流对不上号

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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:

FP=250.562289为什么是在9月结束的时候,画图法能看懂但是现金流老是对不上号,请老师再解释下,谢谢

2 个答案

李坏_品职助教 · 2024年05月04日

嗨,从没放弃的小努力你好:


是的,FP是期初约定的在到期日的成交价。

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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!

李坏_品职助教 · 2024年05月03日

嗨,爱思考的PZer你好:


根据题目的条件,这个forward的期限是9个月。我们现在求的是t=3时刻的value,所以要把t=9这个时刻的FP折现到t=3,也就是往前折现0.5年。

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努力的时光都是限量版,加油!

Kiki · 2024年05月04日

这个FP是约定到期时购买标的资产的价格对吗,所以是支出

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