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Katherine · 2024年04月11日

implied 到底是指bsm模型中输入的波动率还是市场价格中隐含的波动率呀?

NO.PZ2023041003000049

问题如下:

Solomon observes that the market price of the put option in Exhibit 2 is $7.20. Lee responds that she used the historical volatility of the GPX of 24% as an input to the BSM model, and she explains the implications for the implied volatility for the GPX.

Based on Solomon’s observation about the model price and market price for the put option in Exhibit 2, the implied volatility for the GPX is most likely:

选项:

A.

less than the historical volatility.

B.

equal to the historical volatility.

C.

greater than the historical volatility.

解释:

The put is priced at $7.4890 by the BSM model when using the historical volatility input of 24%. The market price is $7.20. The BSM model overpricing suggests the implied volatility of the put must be lower than 24%.

根据强化课,我记得笔记是如果implied 波动率小于市场波动率则buy option 反之则sell。但是这道题将BSM中的波动率称作historical,将市场的称作为implied,,,所以implied 到底是指bsm模型中输入的波动率还是市场价格中隐含的波动率呀?


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已采纳答案

李坏_品职助教 · 2024年04月11日

嗨,爱思考的PZer你好:


implied volatility的定义:

implied volatility指的是从期权的市场价格推算出来的波动率σ,也就是put market price对应的那个波动率。


题目的意思是,这个人先用historical volatility 24%输入到了BSM模型公式里面,得出put的定价是7.489.


但是当前市场上put市场价格是7.2. 7.2的价格对应的波动率σ才是Implied volatility


既然implied volatility对应的期权价格(7.2) < historical volatility对应的期权价格(7.489),说明Implied volatility应当小于historical volatilty 24%.

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