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上小学 · 2023年08月08日

请问题目在讲什么?需要回答啥呢

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.

请问四个选项为何第二个正确,其他都是什么意思呢?题目叙述的是什么?看不懂。谢谢

1 个答案

DD仔_品职助教 · 2023年08月09日

嗨,爱思考的PZer你好:


同学你好,

本题考查结论 - 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。

A不对,不能用ATM的隐含波动率来代替OTM和ATM这个组合的波动率。

B说的是应该用所有期权用BSM公式倒推出的隐含波动率的平均值,这显然是错误的,这章节的名字就要波动率微笑,讲的就是隐含波动率在某些情况下高某些情况下低的问题,题目说了一个OTM和一个ATM的期权,肯定是不能用平均值的。

D不对,因为历史不能代表未来,用历史的波动率不能代表对当前市场的定价是正确的。

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虽然现在很辛苦,但努力过的感觉真的很好,加油!

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