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思思 · 2024年07月13日

还是不理解

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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。

老师,看了解析看的懂,数字理解不了,能否用图表里的数字再解释一遍,多谢

1 个答案

lynn_品职助教 · 2024年07月15日

嗨,努力学习的PZer你好:


解析:印度的NIFTY 50指数当前的交易水平为11610点,因此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。

同学觉得图表不够清楚,究其原因是它没有那么完美,因为说到底这只是一个实证检验的结果,是根据观察真实的市场数据描绘得到的。


那么实务之中的图就有很多种,虽然执行价格为12000的ITM是16.56,但是也有16.39的,而且这两个数字相差不大,在合理的误差范围内,比OTM的17.72小太多了,不符合smile,还是有一个向下倾斜的趋势的。


以put为例,OTM的put隐含波动率高于ATM状态的put;ITM的put其隐含波动率会略微低于ATM状态的put。


16.44 ATM ;17.72 OTM; ITM 16.39

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努力的时光都是限量版,加油!

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