老师有点晕，市场波动率与期权价值成正比。那比如这道题，市场价格小于模型价格，不就是历史波动率小于隐藏波动率吗？

问题如下：

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：

less than the historical volatility.

equal to the historical volatility.

greater than the historical volatility

解释：

A is correct.

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%.

中文解析：

根据市场价格反推出来的波动率叫做隐含波动率；

BSM model中使用的波动率为历史水平的波动率。

波动率与期权的价格呈正向关系，波动率越高，期权越贵。因此现在市场上的期权价格低于BSMmodel计算出来的价格，说明隐含波动率低于历史水平24%。选A。