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上小学 · 2023年08月08日

请问问题和答案都不知道什么意思。

NO.PZ2018122701000088

问题如下:

An empirical distribution of equity price derived from the price of options of such stock based on BSM that exhibits a fatter right tail than that of a lognormal distribution would indicate:

选项:

A.

Equal implied volatilities across low and high strike prices.

B.

Greater implied volatilities for low strike prices.

C.

Greater implied volatilities for high strike prices.

D.

Higher implied volatilities for mid-range strike prices.

解释:

C is correct.

考点 Volatility Smile

解析 An empirical distribution with a fat right tail generates a higher implied volatility for higher strike prices due to the increased probability of observing high underlying asset prices.

请问问题是在说什么?答案的四个选项都是什么意思。谢谢

2 个答案

品职答疑小助手雍 · 2023年08月10日

因为这题给的条件是fatter right tail 右尾肥,这个条件和课上讲的情况是反着的,那结论也就和课上的结论反过来了。

品职答疑小助手雍 · 2023年08月09日

同学你好,本题中,价格密度函数中出现了右尾的情况。既然考察的是右边,我们就要看K2,也就是对应OTM的call而言。

对于call而言,因为本题的假设条件右尾,P{S>K2}的会更高,因此这个call会更贵,因此隐波会更高。因此本题选C。

这题其实就是直接考下图那个lognormal对比的分布,这个算是比较重要的内容了,上课也重点讲过的。

上小学 · 2023年08月09日

股票期权不是左尾肥吗?怎么可能右尾肥呢?讲课说左尾肥。另外,原图说股票执行价格高,波动率低。第一个图不是非常明显吗?为什么我说右边高呢?不是左高右低吗

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