If you don't mind I have two questions for you:
No problem, I don't want you to think I'm some super trader or something. Just a passionate fan of the markets. I'll give it a shot though.
Market is efficient in that there is no arbitrage opportunity? Or is the option market efficient such that the expectancy of someone playing long enough without knowledge is zero?
I think if you observe the general performance of CTAs in the last 30 years we can see that the EMH is more or less not-totally-true.
Arbitrage is sort of ambiguous here. If you mean is there a way to make a risk-free profit? I think so, if you're fast enough. For retails I don't believe there are many arbitrage opportunities you can capitalize on.
If you mean
arbitrage as in
Arbitrage Pricing Theory I certainly think there is significant utility in understanding APT. Even for retails.
Answering this part is relatively difficult because it's pretty opinionated and I do not possess a PhD in financial engineering or economics.
Under the assumption that the expectancy of any trade is zero your argument there is that the markets are approximately martingale. That is, the best estimate of today's return is yesterday's. I don't think this is totally true given the mean reverting properties of some portfolios.
2. How options are priced? MM are the one setting the prices and bid/ask. Armed with simple BSM, all I can see is in the IV number and really no visibility as to how they arrived at that IV. Based on about six months and hundreds if not thousands of trades (covered calls), I could see that their models were very good - I netted about zero minus commissions. If I netted zero, they also netted zero. So they must make money through hedging?
This is an incredibly complicated and interesting question. I can tell you the basic theory of how options are priced but I couldn't tell you how MMs do it.
Options MMs make money primarily through the spread. So your net zero on a one sided trade probably netted them the difference of making that market. As for IV it is
implied because it is determined by the market (and extracted by working backwards from the BSM). They didn't really arrive at the IV so much as the market "priced in" (for lack of a better term) the IV you saw.
Models aren't forced into the BSM world. For example, there is the Bjerksund-Stensland Model (also BSM funny enough) as well as the binomial options pricing model. There are also many jump diffusion models with the BSM. What I am trying to say is simply that we can't know what model the MM you're referring to is using for pricing. We can be almost certain it isn't the Black-Scholes model, however.
I hope this helps. Feel free to shoot me a private message if you want to talk more.