Market makers use a variety approaches

Few, market makers if any, simply buy calls or sell puts when they are bullish and buy puts or sell calls when they are bearish. While most market makers will “scalp” or “leg” into spreads on a short-term basis, trying to take advantage of moves in the underlying prices is not generally their long-term strategy. The risk of simply taking directional bets, or taking on any one kind of exposure for that matter, is just too great; those who do don't survive over the long run.

All market makers attempt to control the risks of their positions, most of them by spreading options against other options or the underlying stock or index futures. Nearly every market maker is looking for a synthetic arbitrage trade – a trade that can be combined with other trades to produce a profit with very low risk.

To do this the market maker must know what is mispriced. In addition he needs to know how to hedge away the unwanted risks. If the market maker can enter two or more offsetting trades that cancel out the risk and do this for a net profit then he solved both problems.

Relative Pricing and Arbitrage Spreads
Market makers often don't need to worry about whether an option is actually over priced or under priced in some absolute sense. What matters is whether an option is mispriced relative to the underlying stock or to other options at any given point in time so they can create a spread and reduce the risk of buying or selling the option.

There are few basic arbitrage spreads that determine the price relationships that the underlying stocks and their various options should have to each other. When these price relationships don't hold, there is an opportunity for profit.  Market makers quickly learn to think in terms of synthetic equivalents –alternative ways of constructing a position. By buying relatively under priced and selling relatively overpriced combinations of puts, calls and stock that have the same risk exposure at the same time, the market maker can take advantage of any mispricing and cancel out his risk. In fact, this basic pricing technique is fundamental part of the way that market makers operate. Looking at option positions in terms of synthetic equivalents tells the market maker his alternatives. It is also key to understanding market makers ability to buy and sell options when the market appears to be heading in one direction and presumably no one else would take the other side.

An example:

Suppose ABC shares are trading at $10.

1.  If you own the stock, you gain and lose a dollar for every dollar the stock rises / falls      above /below $10
2.  If you own a $10 call, at expiry the call is worth a dollar for every dollar above $10
3.  If you're short a $10 put, you position is has lost a dollar for every dollar below $10

So the combination of 2 and 3 a long call and a short put, is synthetically equivalent to 1, owning stock. If the stock price rises a dollar the call is worth a dollar for every dollar above $10 and the short put is worthless. If the stock falls, the long call is worthless and the short put loses a dollar for every dollar below $10.

At expiry the combination of 2 & 3 (long call, short put) will show the same net gain or loss with any change in the stock price. Thus by buying one and selling the other you can eliminate the most significant form of position risk, exposure to the direction of price movement. Buying stock and selling synthetic stock, or the reverse, results in no net direction exposure. The positions cancel because what you make on one you lose on the other.

Not only is there a synthetic equivalent for owning stock, there is a synthetic equivalent for any option or stock position.

Table 1

Position   Synthetic Equivalent
Long Stock Long Call + Short Put
Short Stock Short Call + Long Put
Long Call Long Stock + Long Put
Long Put Short Stock  + Long Call
Short Call Short Stock  + Short Put
Short Put Long Stock  + Short Call

Conversions and Reversals

The two most basic forms of option arbitrage are the “conversion” and reverse conversion or “ reversal”. If a market maker can buy stock and sell synthetic stock (or the reverse) for a net price difference that will more than cover his costs, then the combination of trades ought to make a profit with no directional risk. What matters is not the price of the call or the put or the stock itself in isolation, but the relative prices of the offsetting pieces.

An example:

Suppose a market maker finds the 10 calls, expiring in one month, trading at 45c and the puts at 35c with the underlying trading at $10. The market maker simply puts the three pieces together- selling the call, buying the put and buying the stock. He takes in 10c and at the same time hedges a way his exposure to any changes in the price of the stock. Lets assume that the carrying the stock until expiry costs $10 x  5% x (30/365) = 4c. his net profit on the position, assuming no other costs and no other risks is about 6 cents, which can earned with no price exposure. All calculations should be multiplied by 100 because options cover 100 shares.

There is no reason to think of a conversion exclusively in terms of buying share s and selling them synthetically. From table 1, it is clear that a conversion can be viewed in terms of other pieces. A conversion can be either a long call and a short synthetic call, or a short put and a long synthetic put, as well as long stock and synthetic short stock.

The opposite strategy, a reverse conversion or reversal, can be established if the call and put prices were out of line in the opposite direction. If, for example, the 10 call were offered at 40c and the put bid at 38c, market maker could buy the under priced call, sell the expensive put and sell the stock short for a net debit of 2c. He could then earn interest on the $10 he received from the sale of the stock to generate a net positive return with no directional exposure.

As the current level of interest rates determines whither a conversion or reversal will be profitable these spreads are known as interest rate plays. Using his own appropriate current interest rate, a market maker calculates his cost of carry for the position on including the receipt of the dividend (long stock ) or the payment of one( short stock). He then knows the size of the credit or debit that would make a conversion or reversal profitable, and can examine current option prices with those values in mind.

Market makers are subject to interest rate risk prior to expiry. An increase in rates, increases the cost of carry, a reduction in rates, reduce the size of the interest earned. For this reason market makers generally try to balance the number of conversions and reversals.

Other risks
Changes in implied volatility levels and to dividends are other risks that market makers deal with on an ongoing basis. Whilst neither of these should be underestimated none is as great as directional price risk. Competition among market makers often forces them to accept risks just to be included in trades, however most will not accept directional risk for more than a very short time.