Quote from dmo:
This is a misconception. Market makers don't come up with a mathematical theory or a distribution and then stubbornly stick to it, the market be damned. They just make markets based on the public buying and selling, which is what really creates the skew. Market makers are infinitely pliable.
Here's an example of how it works. Let's say it's the first day ever in the S&P500 options pit. The market makers start off with BS prices. There are 50 days remaining and they're using a volatility of 20%. We'll assume an interest rate of 0 for simplicity. Futures are at 1200. Theoretical prices are as follows:
1100 puts - 5.01
1300 calls - 6.58
Throughout this particular day, the futures don't move. Somebody comes in and asks for a market on the 1100 puts. The market makers make a market of 4.90 bid at 5.10. The public buys a few hundred lots at 5.10. A little later someone else asks for a market in the 1100 puts. The market makers have sold all they want to sell at 5.10. So they give a market of 5.10 bid at 5.30. The customer buys a few hundred at 5.30.
Meanwhile, someone asks for a market on the 1300 calls. MM's give a market of 6.50 bid at 6.70. The public sells a few hundred at 6.50. A little later the public asks for a market again. This time MM's give a market of 6.30 bid at 6.50. The public sells a few hundred more at 6.30.
At the end of the day, it looks like this:
1100 puts - 5.30 bid at 5.50, settle at 5.40 - IV is 20.45%
1300 calls - 6.10 bid at 6.30, settle at 6.20, IV is 19.63%
And voila - we have a skew. Purely the result of market forces - greater buying in the put, greater selling in the calls. This much is known, and indisputable.
The next question is - why is there so much more buying in the put than the call?
At this point objective fact ends and theory begins. Nobody can say with absolute certainty why. It seems obvious to me that it results from the fact that the world is long stock, which puts a premium on the put as insurance against a market decline. But that's just my best guess - I can't prove it.