[First of all, i would like to apologized me for possible language errrors, because i'm from Europe and English is not my mothertongue.] The B&S formula creates "fair option values" as long as the inputs are correct. So the formula predicts that buying or selling options randomly is going to break even in the long run. So buying (or selling) is NOT superior to selling (buying) the same option. That's what the theory says. So if i say that i'm going the sell put options every month without paying attention to implied volatility or a directional market view, what would be the result? The option theorist would say that you will break even in the long run. My point is now, that the practice shows that this is not the case. I refer to the "^put index". The CBOE put/write index systematically sells one-month ATM s&p put options since 1986. The put index has earned a higer return than de S&P 500 (10% average annual return). These result are not in line with what the B&S formula would say? Selling index put option during 26 years was a very profitable strategy and not a 'break-even-strategy'? What are the reason(s) for this deviation (inconsistency)? I have some ideas but i would like to know what you are thinking?
No that is just part of it. The B&S formula relies on a number of big assumptions. The "No arbitrage" assumption is complex and implies things that I don't consider to be very realistic. Every time you use the B&S formula, you're using those assumptions. I doubt there are many practical option traders in the world that blindly follow that formula.
The B&S formula assumes normal distribution, frictionless markets, and other things that don't transfer to real life markets. This is called model risk. It also, to some extent, assumes rational and efficient markets. Bottom line is, if markets worked according to BS, LTCM would still be in business with Myron and Merton on the board. Mathematical models are far from perfect, and they have had implications in several market crashes, including the 2008 crash. So dont take them too seriously. As for selling vs buying, this has been studied extensively. As you say, put writing at ATM on the S&P outperforms the S&P itself. My personal opinion about that, is simply fear is stronger than greed. Thus people are willing to overpay for downside protection, to get rid of said fear. This has to do with market irrationality. If markets really collapsed as often as people thought they would, the CBOE Putwriting index wouldn't outperform the S&P, would it? And Talebs long black swan fund wouldn't be out of business. Just my .02.
The real black scholes implication is that you can synthetically create an option via stock and bonds. This can still hold and listed options not trade at theoretical price that black scholes says it should. Their theory spawned volatlity arbitrage as people would create an option (via delta hedging) and trade the listed option that was at the "wrong" price. All the assumptions: log normal distribution, constant volatility, etc. are close enough to reality but not exact. So opportunities exist. And the reason puts are generally expensive? The world isn't truly risk neutal.