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。
