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四喜 · 2024年05月10日

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NO.PZ201601050100001606

问题如下:

Based on Exhibit 2, the NIFTY 50 Index implied volatility data most likely indicate a:

选项:

A.

risk reversal.

B.

volatility skew.

C.

volatility smile.

解释:

B is correct.

When the implied volatility decreases for OTM (out-of-the-money) calls relative to ATM (at-the-money) calls and increases for OTM puts relative to ATM puts, a volatility skew exists. Put volatility is higher, rising from 16.44 ATM to 17.72 OTM, likely because of the higher demand for puts to hedge positions in the index against downside risk. Call volatility decreases from 12.26 for ATM calls to 11.98 for OTM calls since calls do not offer this valuable portfolio insurance.

A is incorrect because a risk reversal is a delta-hedged trading strategy seeking to profit from a change in the relative volatility of calls and puts.

C is incorrect because a volatility smile exists when both call and put volatilities, not just put volatilities, are higher OTM than ATM.

中文解析:

印度的NIFTY 50指数当前的交易水平为11610点,接近表格2中的11,600。因此可以认为执行价格为11,6000的期权是处在ATM状态的期权。

以看跌期权为例,执行价格高于11600的是ITM的期权;执行价格低于11600的是OTM的期权。

Volatility smile的图形显示的是不论是OTM put还是ITMput,其隐含波动率都是高于ATM状态时的隐含波动率的。

Volatility skew的图形则显示的是OTMput隐含波动率高于ATM状态的putITMput其隐含波动率会略微低于ATM状态的put

因此根据表格可知,这符合volatility skew的形态。

是不是可以简单理解为:只看deep OTM 的 call和put,比较 implied volatility :

差不多相似就是smile,明显有向下趋势就skew呢?

1 个答案
已采纳答案

Lucky_品职助教 · 2024年05月11日

嗨,努力学习的PZer你好:


同学你好:


“差不多相似就是smile,明显有向下趋势就skew呢?” 你这个理解在实际做题的应用中,是没有错的,Volatility smile 和 volatility skew的图形是可以很容易让我们判断出具体情况(见下图)。


Volatility smile以及volatility skew是隐含波动率与执行价格之间表现出来的图形关系,这是一种实证研究的结果,是根据真实的市场数据描绘得到的。


volatility skew通常出现在多头市场,譬如股票市场。对此现象的主流解释为:投资者普遍做多,所以担心会发生价格暴跌,OTM put的需求就会很大,理解为大家都想买个保险,需求推高了价格,使得通过价格反算出来的隐含波动率偏高,形成了skew的形态。


volatility smile通常出现在期货市场,外汇市场,这类多空力量比较均衡的市场。对此现象的主流解释为:OTM put和OTM call需求都比较大,因为过度的上涨下跌都会使一部分参与者出现巨大亏损,所以两侧都会出现隐含波动率偏高的情况。


risk reversal也是策略之一,由卖出一个看跌期权和买入一个看涨期权组成,如下图。risk reversal是一种 delta 对冲的交易策略,从看涨和看跌期权的相对波动性变化中获利。而这道题却是在关注OTM、ATM时的区别。

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