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Rachel杏怡 · 2024年09月18日

讲义 左高右低

NO.PZ2018122701000088

问题如下:

An empirical distribution of equity price derived from the price of options of such stock based on BSM that exhibits a fatter right tail than that of a lognormal distribution would indicate:

选项:

A.

Equal implied volatilities across low and high strike prices.

B.

Greater implied volatilities for low strike prices.

C.

Greater implied volatilities for high strike prices.

D.

Higher implied volatilities for mid-range strike prices.

解释:

C is correct.

考点 Volatility Smile

解析 An empirical distribution with a fat right tail generates a higher implied volatility for higher strike prices due to the increased probability of observing high underlying asset prices.

老师 可以解析一下这个 左高右低的问题吗 ? 我有点搞混了 , 为啥 greater volatility 会 high Strike Price ?

1 个答案
已采纳答案

pzqa27 · 2024年09月18日

嗨,爱思考的PZer你好:


讲义里面说的是在volatility skew(波动率偏斜,股票价格低的时候对应的implied volatility最高),这道题是问了另外一种情况:假如出现了fatter right tail的情况,那么银行波动率和行权价是什么关系?


假如出现了和讲义里相反的fatter right tail,说明股票出现极端的右尾价格的概率(就是突然暴涨)比正常的Lognormal分布的概率要大,右尾价格对应的是行权价格很高的情况,所以是C。


这个题目假设了一种和讲义里相反的情况,讲义里的implied volatility是左高右低,这道题是右边的volatility更高。

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