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小熊猫 · 2025年04月24日

bsm模型可以给这种奇异期权定价吗?

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。

我怎么印象中bsm只可以给欧式期权定价?

1 个答案

李坏_品职助教 · 2025年04月24日

嗨,努力学习的PZer你好:


这道题问的就是BSM模型缺陷是啥。对于这种障碍期权,BSM模型包含的“波动率保持不变”的假设就显得很致命,所以不能用BSM模型。所以A选项说的是缺陷,就选A了。


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努力的时光都是限量版,加油!

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