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积极向上 · 2023年05月29日

Call option 呢?

* 问题详情,请 查看题干

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。

如果以call option为例, 看不到volatility skew的现象呀?

请老师以画图详细解释下


2 个答案

lynn_品职助教 · 2023年11月21日

嗨,爱思考的PZer你好:


“有另外一种理论是,对于OTM put被高估,那么同样执行价格的ITM call根据put call parity也会被高估,拥有较大的implied volatility。”请问老师这句怎么理解呢?题目中 :OTM put (implied volatility 17.72)对应ITM call 5.87,ATM call 12.26,OTM call 11.98, ITM call implied volatility反而最小?另外,可否由implied call volatility 小于put .得出应该short put long call结论?(risk reversal),谢谢老师!


1、因为同样strike price的OTM put被高估,所以通过期权平价理论得知ITM call也被高估了。


2、在volatility smile或者volatility skew的图形中,横坐标是执行价格,纵坐标是隐含波动率。


看跌期权波动率较高,从16.44 ATM升至17.72 OTM,


看涨期权的波动率从ATM看涨期权的12.26下降到OTM看涨期权的11.98


对于ITM 的put option,隐含波动率随着执行价格的升高而下降;对于OTM的call option,隐含波动率随着执行价格的升高而降低的,符合的是volatility skew图形。


3、当put option的隐含波动率相比于call option的隐含波动率被高估时,意味着put option的价格相比于call option被高估,因此可以卖出put option,买进call option。Long risk reversal = long call + short put

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虽然现在很辛苦,但努力过的感觉真的很好,加油!

lynn_品职助教 · 2023年05月30日

嗨,从没放弃的小努力你好:


下面左图是volatility smile,右图是volatility skew


(1)这两个图是实证检验的结果,即我们观察到隐含波动率和执行价格之间就是呈现这种关系。只是呈现的样子不同。


(2)两个图都是反映了option的隐含波动率和执行价格之间的关系。当标的是外汇的时候,一般呈现smile;当标的是股票的时候一般呈现右图的skew(这一点仅作了解即可)。


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。


这也是为什么举例子都是以put option,并不是说call没有这个现象,只能说不典型吧。可以理解为,volatility smile 或者volatility skew都是在实际交易中总结出的一种现象,只不过教材在解释这部分内容的时候使用 OTM put和OTM call来进行说明。


我们看,下面右边这张图,横轴左侧对于call来说就是ITM call,对于put来说就是OTM put,都会出现这volatility smile 或者volatility skew,


有另外一种理论是,对于OTM put被高估,那么同样执行价格的ITM call根据put call parity也会被高估,拥有较大的implied volatility。


顺便再讲一下,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。




----------------------------------------------
虽然现在很辛苦,但努力过的感觉真的很好,加油!

fresh · 2023年11月21日

“有另外一种理论是,对于OTM put被高估,那么同样执行价格的ITM call根据put call parity也会被高估,拥有较大的implied volatility。”请问老师这句怎么理解呢?题目中 :OTM put (implied volatility 17.72)对应ITM call 5.87,ATM call 12.26,OTM call 11.98, ITM call implied volatility反而最小?另外,可否由implied call volatility 小于put .得出应该short put long call结论?(risk reversal),谢谢老师!

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