I understand that bid/ask prices and bid/ask sizes are ultimately determined by the market maker. I am curious about some general principles that the market maker follows when determining the above parameters.
If the market maker is just a middle man, why should he take pains to figure out these values, so long as he is collecting money every time a trade happens?
First, there are some general principles one should be aware of regarding market makers:
If a security has been trading, it's easy for a new market maker to come in and post orders. Most of it's now computer generated, so the computer will look at the last trade or the mid-point of the bid/ask and post its' own bid & ask and adjust them accordingly once one of the MM's orders is filled.
If an ask is hit, they will continue to post asks but at much higher prices because they will be overloaded with shorts. They will take into account the volume and try to make some sort of estimate of how wide the spread they offer should be, X. They will post a bid at (1-X)*ask. If their asks continue to get hit, they will take the average price of all sales and multiply them by that X thus moving up their bid albeit at a much slower rate than their asks since they are becoming overloaded with shorts.
Except for pink sheets and otcbbs, this process is well-handled in advance for the market maker in the form of IPOs where many auctions leading up to the listing take place for the market makers to analyze.
For short-dated options, the MMs typically try to latch on to the implied volatility of the mid-point of their bids & asks to the historical volatility over the same period.
It goes on and on from there, but those are the basics. Reality is a little different because volume typically rushes from one side to the other, and the MMs try to accommodate for fear of losing business or being kicked off the exchange. For options, the only real fear MMs have are sudden moves in the underlying more than the IV they've accepted that hasn't been priced to absorb that kind of move.
Also, just to clarify, the MMs do not determine the prices of the securities. They are only half of the equation when they actually trade. In highly liquid assets, it could just as easily be speculator to speculator, and if the MMs are not posting prices that anyone wants to hit, they aren't trading at all.
Market makers always face adverse selection risk (or risk "getting run over" in the parlance), in the sense that they are more likely to have sold a security just before the market clearing price increases or bought a security just before the market clearing price decreases.
Accordingly, deciding on a spread between one's (possibly multiple) bids and offers and the sizing of those quotes plays a role in determining the ultimate profitability of that market maker.
To do so, it is useful to have an idea on how the probability of trading on either side of the market (one's bids getting hit or offers getting lifted) varies with the distance one places bids and offers away from the mid price (measured by some combination of cents and depth). Basically, there are probably many ways of trying to model this, many of which are proprietary, but there is a growing body of public literature detailing approaches to solving these problems, for example Avellaneda & Stoikov's paper "High Frequency Trading in a Limit Order Book", Lehalle et al with "Dealing with Inventory Risk" and more recently Fodra's "High frequency market making with inventory constraints and directional bets".
The maths in the above is pretty heavy for someone who doesn't have reasonably exposure to working with differential equations (and that unfortunately includes me).
