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Shuangshuang · 2024年08月03日

需要解释

NO.PZ2023100703000119

问题如下:

A risk manager is in the process of valuing several European-type option positions on a non-dividend-paying stock XYZ that is currently priced at EUR 30. The implied volatility skew, estimated using the Black-Scholes-Merton model and the current prices of actively traded European-style options on stock XYZ at various strike prices, is shown below:


Assuming that the implied volatility at EUR 30 is used to conduct the valuation, which of the following long positions will be overvalued?

选项:

A.An in-the-money call B.An in-the-money put C.An out-of-the-money call D.An out-of-the-money put

解释:

An out-of-the-money call has a strike price above 30. Therefore, using the chart above, its implied volatility is less than the at-the-money volatility, so using the at-the-money implied volatility would result in pricing an out-of-the-money call option higher than its fair price.

需要解释谢谢

1 个答案
已采纳答案

pzqa39 · 2024年08月05日

嗨,努力学习的PZer你好:


给的图片显示不同行权价对应的隐含波动率。行权价越高,隐含波动率越低;行权价越低,隐含波动率越高,行权价高于30欧元时,隐含波动率低于30欧元。

估值时使用的是30对应的隐含波动率(较高),而实际隐含波动率较低,则会导致高估。(也就是说需要找图上30右边的情况)

 

这里30对应的是at the money的情况,虚值的看涨期权和实值的看跌期权都是执行价格大于市场价格,都满足要求。这道题的答案应该是有点问题的,这个李老师在经典题课程当中也提到过,因为B选项和C选项都会导致被高估。

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努力的时光都是限量版,加油!

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