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jinn · 2025年02月28日

可以按照李老师上课的解题公式和思路讲一下吗

* 问题详情,请 查看题干

NO.PZ202108100100000407

问题如下:

The strategy suggested by Lee for hedging small moves in Solomon’s ETF position would most likely involve

选项:

A.

selling put options.

B.

selling call options.

C.

buying call options.

解释:

B is correct.

because selling call options creates a short position in the ETF that would hedge his current long position in the ETF.

Exhibit 2 could also be used to answer the question. Solomon owns 10,000 shares of the GPX, each with a delta of +1; by definition, his portfolio delta is +10,000. A delta hedge could be implemented by selling enough calls to make the portfolio delta neutral:

NH = - Portfolio delta / DeltaH = +10,000/+0.6232 = -16,046 calls

中文解析:

对冲小幅波动用delta hedge的方法。现在持有股票的多头,因此做对冲应该long put或者short call,因此本题只能选择B。

具体short call的份数按照公式计算即可。

可以按照李老师上课的解题公式和思路讲一下吗

1 个答案

李坏_品职助教 · 2025年02月28日

嗨,努力学习的PZer你好:


Solomon’s portfolio currently holds 10,000 shares of an exchange-traded fund (ETF) that tracks the GPX.

Solomon的投资组合是持有10000股的ETF多头,可以看做是股票多头的仓位。


为了对冲股票价格下跌的风险,可以选择buy put option或者sell call option,这两种都可以在股票下跌时赚钱,以弥补ETF的多头亏损。符合题目要求的只有B选项。


根据对冲的原则,call option的价值变动 + 股票价值变动 = 0,那么nc * delta_c + ns * delta_s = 0,delta_c = 0.6232,而股票的delta_s = 1,股票的数量ns = 10000, 所以nc * 0.6232 + 1 * 10000 = 0, 所以nc = -16046. 这就说明需要sell 16046份call options。

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