Which of the following statements is INCORRECT?

a$.$

Trading shares of the underlying stock will not affect either the gamma or the vega of a portfolio.

b$.$

In a $$volatility smile$,$ all options have the same expiration date, but they have different strike prices.

c$.$

Black$-$Scholes model assumes that the yield curve is flat.

d$.$

None of the above $($all are correct$)$