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seven-zhu · 2021年08月02日

No.PZ2018122701000085

NO.PZ2018122701000085

问题如下:

Below are statements about equity option volatility:

I.Deep out-of-the money options have higher implied price volatility than at-the-money options.

II.“Crashophobia” is a phenomenon which actual stock prices in the market decease sharply and volatility increases

III.In comparison with the lognormal distribution, the equity option volatility has the same probability of large downward movements and large upward movements.

IV.An increase in leverage if stock price goes down will increase the volatility

The most appropriare statement(s) is /are:

选项:

A.I and II B.III and IV C.II and III D.IV only

解释:

D is correct.

考点 Volatility Smile

解析

I is incorrect. There is higher implied price volatility for low strike price equity options. For call option, deep in-the-money option has higher implied price volatility, but for put option, deep out-of-the money options have higher implied price volatility.

II is incorrect. "Crashophobia" is based on the idea that large price declines are more likely than assumed in Black-Scholes-Merton prices, not that volatility increases when prices decline.

III is incorrect.Compared to the lognormal distribution, traders believe the probability of large down movements in price is higher than large up movements.

IV is correct. Increasing leverage at lower equity prices suggests increasing volatility.

可以详细解释下第三为什么是错的吗~

1 个答案

品职答疑小助手雍 · 2021年08月02日

嗨,从没放弃的小努力你好:


因为根据volatility smile,股票期权的implied volatility是不对称的~

所以3说交易者认为上涨下跌的可能性一样就肯定是错的啦。

至于哪种可能性高,有很多种思路。

根据波动率微笑,股票期权低strike price的implied volatility更大一些。同一只股票来说,用BSM模型推论,一个50strike 的call 和一个55 strike的call,隐含波动率是50的高,那波动率越高价值越大,所以波动率给50的期权带来的价值比55的大,意味着交易者更愿意去买50的期权(才导致其隐波高),他们觉得55的可能行不了权,而50的可以行权。即他们觉得低价的可能性更大。

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