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世纪之龙5 · 2024年03月17日

ac区别在哪里

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。

如题

2 个答案
已采纳答案

李坏_品职助教 · 2024年03月17日

嗨,爱思考的PZer你好:


A说的是:对于up-and-out期权(这个是股价涨过某个价位后,该期权会立刻被敲出,也就是会自动失效),如果敲出价位与行权价格相等,那么BSM模型是假设隐含波动率变化不敏感的。这个的确属于BSM的一个缺陷。


C说的是:对于down-and-out期权(这个是当股价跌破某个价位后,会被敲出失效的期权),如果敲出价格小于行权价,那么BSM模型对期权的到期期限不敏感。这个说法是不对的。当敲出价格小于行权价时,期权依然是正常存续的,暂时不会失效,此时BSM依然可以使用,所以C项不是BSM的缺陷。

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世纪之龙5 · 2024年03月18日

为什么当敲出价格小于行权价时,期权依然是正常存续的

李坏_品职助教 · 2024年03月18日

嗨,从没放弃的小努力你好:


因为down-and-out只有在股价跌破敲出价格的时候,期权才失效。现在是股价(行权价附近)大于敲出价格,所以期权还是正常生效的。

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