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郎布斯吃苹果 · 2023年01月20日

结合题干，B的分析没看懂

  1. CFA III
  2. Derivative

* 问题详情，请 查看题干

NO.PZ202208100100000104

问题如下：

In her statement to Patel, Cho is most likely correct regarding the:

选项：

A.

volatility skew.

B.

volatility smile.

C.

risk-reversal strategy.

解释：

A is correct. Cho correctly describes the volatility skew. Implied volatility for out-of-the-money (OTM) put options is higher than for at-the-money (ATM) put options and increases as the strike price moves further away from the current stock price. Implied volatilities for OTM call options are lower than for ATM call options and decrease as strike prices rise above the current stock price.

B is incorrect. Cho is incorrect about the volatility smile. The volatility smile occurs when OTM call and put option volatilities are higher than ATM option volatilities and are also higher than normal volatilities for OTM put and call options.

C is incorrect. Cho is incorrect about the long risk-reversal strategy; in fact, she describes a short risk-reversal strategy. If the put-implied volatility is too high relative to call-implied volatility, you would devise a long risk-reversal strategy by shorting the out-of-the-money put option and go long the out-of-the-money call option.

如题

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郎布斯吃苹果 · 2023年01月20日

B错的原因是否是volatility smile图形是波动率和执行价格关系，和当前股票价格无关？

1 个答案

Hertz_品职助教 · 2023年01月20日

嗨，努力学习的PZer你好：


同学你好

关于volatility smile，题干的描述是：However, sometimes implied volatility decreases for put options at strike prices that are lower than the current stock price, whereas implied volatilities increase for call options at strike prices that are higher than the current stock price; this is called the volatility smile.

翻译过来就是说：当执行价格低于当期股价时，看跌期权的隐含波动率会下降;而当执行价格高于当期股价时，看涨期权的隐含波动率会上升;这就是所谓的波动微笑。


错误的地方在我加粗之处，因为：

对于volatility smile来说，当执行价格低于当前股价时，put option的隐含波动率是在增加的，这一点和volatility skew是一样的；当执行价格高于当前股价的时候，call option的隐含波动率也是在上升的，因此题干中的表述错误。

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虽然现在很辛苦，但努力过的感觉真的很好，加油！

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