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GQ · 2024年11月07日

老师麻烦解释一下这道题吧

NO.PZ2023041003000059

问题如下:

Madisox notes that the implied volatility for the Weehawkin call option outlined in Exhibit 2 is 30%. With respect to other call options on Weehawkin stock, Madisox states the volatility surface provides a visualization of how implied volatility varies across both exercise price and time to maturity. Burr adds that implied volatility is useful in assessing the market price of risk since it is calculated on the basis of the historical volatility in the stock price. Jeffinsin concurs and adds that the volatility smile and skew typically have identical shapes whenever the market price of hedging is rising.

Whose comment regarding implied volatility is most likely correct?

选项:

A.

Burr’s

B.

Madisox’s

C.

Jeffinsin’s

解释:

Madisox’s statement is correct. Implied volatility is a measure of future estimated volatility, which varies across both exercise price and time to expiration for various options. Accordingly, implied volatility is a measure of the market price of risk.

A is incorrect. Burr’s statement is incorrect. Implied volatility is a measure of estimated future volatility, not historical volatility. Implied volatility is not calculated on the basis of historical volatility. Rather, implied volatility is a component of an option pricing model.

C is incorrect. Jeffinsin’s statement is incorrect. Volatility skew tends to steepen whenever the market price of hedging is rising, which causes its shape to be different from the volatility smile.

不太理解

1 个答案

李坏_品职助教 · 2024年11月07日

嗨,爱思考的PZer你好:


题目最后问你,哪个人关于implied volatility(隐含波动率)的说法是正确的?

Madisox:波动率曲面告诉我们,隐含波动率是怎样随着执行价格和剩余期限而变化的。这个是对的。波动率曲面(volatility surface)是三个坐标构成的立体3D图,分别是volatility,exercise price,time to maturity。


Burr:隐含波动率在对市场风险进行评估的时候很有用,因为隐含波动率是根据股票价格的历史波动率计算出来的。这个错误。隐含波动率是把期权的市场价格、无风险利率、剩余期限、执行价格等参数,输入到BSM期权模型中,反推出σ(就是股票的标准差),这个σ就是隐含波动率。这是通过BSM反向推出来的,和历史波动率不相干。


Jeffinsin:波动率微笑,和波动率偏斜,在市场价格上升的时候,有相同的形状。这个错误。

波动率偏斜(skew)两边是不对称的,而波动率微笑(smile)两边是对称的,这俩形状不一样。



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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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