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hillock1122 · 2020年02月29日

问一道题:NO.PZ2016070201000041 [ FRM II ]

问题如下:

Kirk Rozenboom, FRM, uses the Black-Scholes-Merton (BSM) model to value options. Following the financial crisis of 2007-2009, he is more aware of the limitations of the BSM option pricing model. Which of the following statements best characterizes a major limitation of the BSM option pricing model?

选项:

A.

The BSM model assumes strike prices have nonconstant volatility.

B.

Option traders often use a volatility smile with lower volatilities for out-of-the- money call and put options when applying the BSM model.

C.

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

D.

For down-and-out calls and puts, the BSM model is insensitive to changes in option maturity when the knock-out strike price is greater than the strike price and the interest rate is greater than the underlying asset return.

解释:

C is correct. For up-and-out calls and puts and for down-and-out calls and puts, the BSM option pricing model is insensitive to changes in implied volatility when the knock-out strike price is equal to the strike price and the interest rate equals the underlying asset return. The BSM model assumes strike prices have a constant volatility, and option traders often use a volatility smile with higher volatilities for out-of-the-money call and put options.

这道题是问用BSM来给期权定价的缺点或者局限吗?B和C想要表达的是市场上的波动率是变化的,而BSM假设波动率不变,所以有局限,对吗?只不过B说反了,C表述的情形是对的。

1 个答案

orange品职答疑助手 · 2020年02月29日

同学你好,你的理解没错