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小爽加油呀 · 2023年07月31日

ABC

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。

A,insentive to change in implied volitility, BSM是假设volatility相同吧?所以A为啥对

c,一个option maturity,不懂

B,为啥错

D错是因为volitility应该不变吧

4 个答案

品职答疑小助手雍 · 2023年07月31日

D错是因为说错的BSM的假设,也不是它的limitation,所以不选。

品职答疑小助手雍 · 2023年07月31日

C说的期权是随着股票价格跌破某个点,期权立刻作废。C选项说的是当这个作废价位(knock out strike)低于普通的行权价的时候,此时期权依然是正常存续的,此时BSM依然可以用,不会出现A项的问题,所以C项不是BSM的缺陷,C项不对。

品职答疑小助手雍 · 2023年07月31日

B选项说法和股票期权volatility smile的结论违背,ITM的call,隐波是高的,但是这和BSM的局限性没关系,所以不选。

品职答疑小助手雍 · 2023年07月31日

同学你好,A里面的knock-out option是指的随着标的资产(股票)价格上涨到一个价位的时候,期权立刻失效作废。这种期权,当靠近konck-out价位的时候,期权价格对于隐含波动率的一点点变化都会很敏感(因为期权随时可能作废)。而BSM假设隐含波动率不变,对于这种期权的定价来说就是致命伤了。

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