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金融民工阿聪 · 2021年01月31日

这章好像讲义都没涉及这个期权和波动率的关系

  1. FRM II
  2. Market Risk Measurement And Management

NO.PZ2020033001000041

问题如下：

Which of the following statements best illustrates the main limitations of the BSM option pricing model?

选项：

A.

For up-and-out calls and puts, when the knock-out strike price is equal to the strike price and the interest rate is equal to the return on the underlying asset, the BSM model is insensitive to changes in implied volatility.

B.

The volatility smile indicates that the implied volatility of in-the-money call and put options is relatively low.

C.

For down-and-out calls and puts, when the knock-out strike price is smaller than the strike price and the interest rate is higher than the return on the underlying asset, the BSM model is not sensitive to changes in option maturity.

D.

The BSM model assumes that volatility changes as the market changes

解释：

A is correct.

考点：BSM模型的缺点

解析：作为结论了解即可：因为BSM假设的是constant volatility，但是实际中，在knock out价等于行权价，以及underlying收益率等于利率时，期权价格对隐含波动率会很敏感。因此BSM的假设隐含波动率变化不敏感就是模型的缺陷。

像这类期权和波动率关系的题，一般压力怎么判断呢，特别是涉及out/in-the-money的call/put对于波动率的影响，还有BSM模型和隐含波动率的关系

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小刘_品职助教 · 2021年02月01日

同学你好，

首先BSM模型和隐含波动率的关系，由期权价格，根据BSM模型倒算出的波动率就是隐含波动率。

因为BSM模型假设波动率是恒定的，所以就可以从历史观测出来的期权价格倒算出隐含波动率之后然后算出新的期权价格。

对于期权和波动率的关系，建议在做的时候去思考一下，这个期权是否处于不行权和行权的边缘，如果是的话，那他对波动率就是十分敏感的，这个时候在使用BSM的时候就得注意。

对于这道题的A和C，奇异期权现在已经不是FRM二级考察的内容了，可以直接忽略，想记结论也没问题。

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