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410140980 · 2023年07月03日

euity option volatility

NO.PZ2018122701000091

问题如下:

A risk manager is examining a firm’s equity index option price assumptions. The observed volatility skew for a particular equity index slopes downward to the right. Compared to the lognormal distribution, the distribution of option prices on this index implied by the Black-Scholes-Merton (BSM) model would have:

选项:

A.

A fat left tail and a thin right tail.

B.

A fat left tail and a fat right tail.

C.

A thin left tail and a fat right tail.

D.

A thin left tail and a thin right tail.

解释:

A is correct.

考点 Volatility Smile

解析 A downward sloping volatility skew indicates that out of the money puts are more expensive than predicted by the Black-Scholes-Merton model and out of the money calls are cheaper than expected predicted by the Black-Scholes-Merton model. The implied distribution has fat left tails and thin right tails.

老师股指期权的隐含波动率是皮笑肉不笑的smirk图形,对于call option那么在执行价低的时候implied volatility高,所以期权比较贵,到这我都理解,怎么对应到表的资产equity的price distribution上的呢?又怎么去判断肥尾瘦尾的呢?

1 个答案

李坏_品职助教 · 2023年07月03日

嗨,努力学习的PZer你好:


Implied distribution指的是:假如implied volatility是真实的股票波动率的情况下,推导出来的股票分布。


假如implied volatility是真实的波动率,那么意味着市场上大部分人都愿意去赌“低股价”。也就是说大家认为低股价的发生概率远高于正态分布,也就是市场上认为的左尾分布大于正态分布理论的左尾,所以有fat left tails。

同理,smirk揭示的波动率下,高股价的发生概率小于正态分布,所以是thin right tails。

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