How do market makers price options? (In depth)
So before you think this question is basic and answered a million times, I've read many responses on reddit and elsewhere and haven't seen any in-depth answers to my specific questions, and/or I see conflicting answers. 1. what role does supply/demand play in options' pricing since it can conflict with the actual cost to delta hedge an option? If supply outweighs demand I can't imagine a MM selling for less than it'll cost to delta hedge the option. 2. How are ITM/OTM options priced? I've read it's based off the vol skew using ATM prices, though a vol skew would be the result of OTM/ITM prices, not the cause. Otherwise how would you determine the skew? 3. Empirically, variance doesn't scale linearly nor is it stationary. So in reality a stock can have 20% monthly variance, but 2% daily variance. If you were to scale the daily up to monthly (.02*30) it'd be 60%. A 1 month DTE option cannot be priced off of √20% IV because the daily variance will make it more expensive to hedge than that throughout its life. This can go further, minute or second or even every tick prob has different annualized variance, so which one do MM use to find IV? 4. All of these assume MM price options based off cost to hedge because idk how they couldn't so correct me if I'm wrong. If MM price based on cost to hedge (IV), and the sum of every strike's IV can create an implied prob distribution of the underlying at expiration, wouldn't they sometimes conflict? Meaning they'd have to price at x because it's the cost to hedge, but pricing at x under or overstates the probability density at that point in the PDF? Thanks for answering