Problem $4.$ If we get a wrong $$ in the Black Scholes Model: $($Select all that apply.$)$

a$.$ We will get a wrong option price

b$.$ We will get a wrong delta$-$hedging strategy

c$.$ We will absolutely lose money because of the wrong hedging

Please explain your answer.

Problem $5.$ Which of the followings will cause problems in BSM$?$ Select all that apply.

a$.$ Security returns tend to have fatter tails than $log$ normal distribution

b$.$ The volatility surface is not flat

c$.$ Distribution of stock returns are not I.I.D$.$ in the practice

Please explain your answer.

Problem $6.$ According to the volatility surface:

a$.$ options with a lower strike tend to have high implied volatility

b$.$ the implied volatility must be lower for longer time$-$to$-$maturity

Please explain your answer.