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考拉 · 2024年02月01日

implied volatility of 21.05%是怎么算出来的？

  1. CFA III
  2. Derivative

* 问题详情，请 查看题干

NO.PZ202208100100000702

问题如下：

With regard to the strategy for Company A that Fillizola recommends, she is least likely correct regarding:

选项：

A.

the expectation of volatility of the underlying.

B.

the effective sale price if share prices move lower, to $130.

C.

the effective sale price if share prices trend higher than $140.

解释：

Solution

A is correct. Fillizola is incorrect regarding the expectation of volatility of the underlying compared with the implied volatility of 21.05%. The recommended strategy, a covered call, is appropriate if the expectation is that volatility of the underlying will be lower than the implied volatility of 21.05%. Fillizola is correct about the effective sale price if the stock is above $140. The stock gets called away at $140, and the effective sale price is $140 + $5.40 = $145.40. If the share price is $130, the client will sell at $130 and her effective sale price is $130 + $5.40 = $135.40.

B is incorrect. Fillizola is correct about the effective sale price. If the share price is $130, the client will sell at $130 and her effective sale price is $130 + $5.40 = $135.40.

C is incorrect. Fillizola is correct about the effective sale price if the stock is above $140. The stock gets called away at $140, and the effective sale price is $140 + $5.40 = $145.40.

中文解析：

本题考察的是covered call。

题干大意：一个客户拥有2000股公司A的股票，该股票不支付股息，目前定价为139.81美元。但是客户被禁止出售该股票。客户预计股价在未来几个月保持稳定，虽然不能出售，但仍希望获得一些收入。

因此Fillizola建议客户卖出20份的到期时间在2020年二月份的看涨期权，这个看涨期权的执行价格是140美元，期权费是5.4美元，隐含波动率是21.05%。

由于该客户本身持有股票，如果再short call，那么构成了covered call策略。因为期权与隐含波动率成正相关关系，short option在这里short call，意味着是看跌波动率的，即预测市场是平稳的，所以表述中关于波动率的表述（预测股价波动率将会高于21.05%）是错误的，选A。

当股价高于140美元时，long call的一方会行权，那么我们需要将手里的股票按照140美元的价格卖给对手方，但是一开始卖出call option获得期权费是5.4美元，因此有效的卖出价格是145.4美元，C选项正确；

如果股价是130美元，那么long call的一方不会行权，如果我们要卖出股票的话，只能按照130美元卖出，但是short call获得了5.4美元的期权费，因此有效的卖出价格是135.4美元。B选项正确。

A is correct. Fillizola is incorrect regarding the expectation of volatility of the underlying compared with the implied volatility of 21.05%. The recommended strategy, a covered call, is appropriate if the expectation is that volatility of the underlying will be lower than the implied volatility of 21.05%.

文章前后都没出现高于或者低于21.05%，也不知道21.05%是怎么算的，对解题思路有点摸不透

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1 个答案

pzqa31 · 2024年02月02日

嗨，从没放弃的小努力你好：


题干条件直接给的：“Fillizola notes that this strategy would be appropriate only if the expectation of the stock’s volatility is higher than the implied volatility of 21.05%.”

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NO.PZ202208100100000702 问题如下 With regarto the strategy for Company A thFillizola recommen, she is least likely correregarng: A.the expectation of volatility of the unrlying. B.the effective sale priif share prices move lower, to $130. C.the effective sale priif share prices trenhigher th$140. SolutionA is correct. Fillizola is incorreregarng the expectation of volatility of the unrlying comparewith the implievolatility of 21.05%. The recommenstrategy, a coverecall, is appropriate if the expectation is thvolatility of the unrlying will lower ththe implievolatility of 21.05%. Fillizola is correabout the effective sale priif the stois above $140. The stogets calleaw$140, anthe effective sale priis $140 + $5.40 = $145.40. If the share priis $130, the client will sell $130 anher effective sale priis $130 + $5.40 = $135.40.B is incorrect. Fillizola is correabout the effective sale price. If the share priis $130, the client will sell $130 anher effective sale priis $130 + $5.40 = $135.40.C is incorrect. Fillizola is correabout the effective sale priif the stois above $140. The stogets calleaw$140, anthe effective sale priis $140 + $5.40 = $145.40. 中文解析本题考察的是coverecall。题干大意一个客户拥有2000股公司A的股票，该股票不支付股息，目前定价为139.81美元。但是客户被禁止出售该股票。客户预计股价在未来几个月保持稳定，虽然不能出售，但仍希望获得一些收入。因此Fillizola建议客户卖出20份的到期时间在2020年二月份的看涨期权，这个看涨期权的执行价格是140美元，期权费是5.4美元，隐含波动率是21.05%。由于该客户本身持有股票，如果再short call，那么构成了coverecall策略。因为期权与隐含波动率成正相关关系，short option在这里short call，意味着是看跌波动率的，即预测市场是平稳的，所以表述中关于波动率的表述（预测股价波动率将会高于21.05%）是错误的，选A。当股价高于140美元时，long call的一方会行权，那么我们需要将手里的股票按照140美元的价格卖给对手方，但是一开始卖出call option获得期权费是5.4美元，因此有效的卖出价格是145.4美元，C正确；如果股价是130美元，那么long call的一方不会行权，如果我们要卖出股票的话，只能按照130美元卖出，但是short call获得了5.4美元的期权费，因此有效的卖出价格是135.4美元。B正确。 能不能一下这里的考点以及相关的讲义

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2023-02-13 22:09 1 · 回答