Basic questions on Black-Scholes

If we assume all Black-Scholes assumptions hold including flat volatility and continuous-time movements, for someone selling options and delta-hedge, does the option moneyness choice matter at all? It seems to me in a typical textbook delta-hedge example, it doesn't matter if one sells a 95 call, 100, or 108 call.

 

If you believe in random walk theory maybe it doesn't make a difference.

 

no. Expected value is all the same.

 

Black and Sholes is wrong ...

 

If you are right you have a major advantage when entering a trade.

 

There is volatility smirk ...

 

doesn’t prove black scholes is wrong.

 

I meant, that you are right. The expected value of all the strikes is the same and you are indifferent to which strike you trade.

 

If, as you mentioned, the original BS assumptions hold then your continuous time delta hedging is just trading a replicating portfolio in which it does not matter which strike you choose.

 

agreed. given the assumptions it doesn't matter. prior to black monday, I think that was the case