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EmilyZhou · 2025年05月07日

老师麻烦解释一下这道题,没有明白题目考查的是什么?

NO.PZ2025040202000002

问题如下:

A trader engages in a strategy that replicates the payoff of a long position in a put option within a single-period binomial framework. At time step 0, the cash flow is:

选项:

A.A.negative. B.B.zero. C.C.positive.

解释:

A Incorrect because the trading strategy that will generate the payoff of taking a long position in a put option is to short sell -h=-(p+-p-)/(S+-S-) units of the underlying and financing of -PV(-hS-+p-). Because p+ is less than p-, the hedge ratio is negative. With h negative, the trade is a short sale, and because -h is positive, the value -hS results in a positive cash flow at Time Step 0. Therefore, the cash flow is not negative.

B Incorrect because the trading strategy that will generate the payoff of taking a long position in a put option is to short sell the underlying and financing, therefore, the cash flow is not zero.

C Correct because the trading strategy that will generate the payoff of taking a long position in a put option is to short sell -h=-(p+-p-)/(S+-S-) units of the underlying and financing of -PV(-hS-+p-). Because p+ is less than p-, the hedge ratio is negative. With h negative, the trade is a short sale, and because -h is positive, the value -hS results in a positive cash flow at Time Step 0.

老师麻烦解释一下这道题,没有明白题目考查的是什么?

1 个答案

李坏_品职助教 · 2025年05月07日

嗨,努力学习的PZer你好:


题目要求在期初,复制一个long put option,而且要用binomial model去复制。

根据基础班讲义里面的公式,long put就是P = hS + PV。

这个h是负数的,所以相当于期初short 一些股票。short股票就是从机构手里借入一些股票卖出,这样可以得到一笔钱,再把这个钱进行投资,这样就有了后面的PV。 这两部分组合起来就复制出了long put option的效果。


题目问你,期初现金流是正的还是负的?既然我们short 股票得到了钱,那说明期初现金流是positive的,选C。


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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!

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