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很不酷 · 2021年01月18日

问一道题:NO.PZ2018122701000086

问题如下:

You are asked to mark to market a book of plain vanilla stock options. The trader is short deep out-of-money options and long at-the-money options. There is a pronounced smile for these options. The trader’s bonus increases as the value of his book increases. Which approach should you use to mark the book?

选项:

A.

Use the implied volatility of at-the-money options because the estimation of the volatility is more reliable.

B.

Use the average of the implied volatilities for the traded options for which you have data because all options should have the same implied volatility with Black-Scholes and you don’t know which one is the right one.

C.

For each option, use the implied volatility of the most similar option traded on the market.

D.

Use the historical volatility because doing so corrects for the pricing mistakes in the option market.

解释:

C is correct.

考点 Volatility Smile

解析 The prices obtained with C are the right ones because they correspond to prices at which you could sell or buy the options.

麻烦解释一下题干,看不明白在做什么。

1 个答案

小刘_品职助教 · 2021年01月19日

同学你好,

这道题考察的就是一个结论,了解即可。

题干的意思是你现在需要对一个组合进行估值,这个组合是由两个期权组成,一个是short deep out-of-money option,另一个是long at-the-money option。这两个期权有波动率微笑,因此隐含波动率是变化的,所以不能两个期权合并定价,需要分别用对应的隐含波动率进行定价。

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