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toffee · 2023年05月21日

而且这个题的角度也很奇怪?

* 问题详情,请 查看题干

NO.PZ202208100100000203

问题如下:

In his statement to Calzada, Armitage is least likely correct with regard to:

选项:

A.

delta hedging.

B.volatility smile.

C.

long risk reversal.

解释:

Solution

B is correct.

Exhibit 2 depicts a volatility skew in which implied volatility increases for out-of-the-money (OTM) put options and decreases for OTM call options. A volatility smile occurs when the curve is U-shaped––that is, implied volatility increases for OTM puts and calls.

C is incorrect. Armitage is correct about the long risk reversal strategy of selling the OTM put and buying the OTM call if the put implied volatility is considered to be too high compared with the call implied volatility.

A is incorrect. Armitage is correct about delta hedging the option position by selling the underlying asset.

中文解析:

本题考察的是volatility skewrisk reversal以及delta hedge

B选项:

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。

根据ATM一列,可以得到当前股价是17.60,此时的隐含波动率认为是100%(表格中省略)。

对于put option来说:执行价格为26.31和执行价格为22.40时,都是ITM的。

且执行价格越高(26.31),越deep ITM,其隐含波动率越低(80%)。

对于call option来说:执行价格为15.5414.65都是OTM的,且执行价格越低(14.65),越 deep OTM,其隐含波动率越高(120%)。

综上:对于ITM put option,隐含波动率随着执行价格的升高而下降;对于OTMcall 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。

C选项: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 optionLong risk reversal = long call + short put,因此C选项没有问题。另,short risk reversal = long put + short call

A选项:调整手里头寸的delta通过交易股票来实现,这里题干说的不是很清楚,因为是否是卖股票,要看手里的头寸的delta以及想要达到的目标delta值来判断,这里就把题干的意思理解为可以通过买卖股票来调节delta即可,因为关于volatility smile的判断是明显错误的。(本题出的不是很好,建议了解即可)

老师上课讲,判断volatility skew 只要是要看 OTM 的 put 和 OTM 的call 这里面给的数据 全是ITM的 这样判断 也可以吗?

1 个答案

pzqa31 · 2023年05月22日

嗨,努力学习的PZer你好:


横轴左侧对于call来讲就是ITM call,对于put来讲就是OTM put,相反的,横轴右侧对call来讲是OTM call,对put来讲是ITM put。

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。

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toffee · 2023年05月23日

明白了,就是ITM的情况也得留意下

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