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.
老师请问下
volatility smile说的是个啥啊，使用BSM model为啥要用volatility smile with lower volatilities for out-of-the- money call and put options？
敲出价格等于执行价格BSMmodel对V的改变肯定是敏感的，后句怎么理解啊 interest rate equals the underlying asset return?
为敲出价格远离执行价格，所以时间长也无所谓，insensitive可以理解，后句怎么理解啊interest rate is greater than the underlying asset return?
