An important theory in options pricing is Put/Call Parity.  This means that the value of a call option implies a certain fair value for the corresponding put, and visa versa.  The entire argument for this pricing relationship relies on arbitrage.  If the value of puts and calls were to diverge, arbitrageurs would step in to eliminate any departure from put call parity.

This relationship is strict only for European-style options, but the same concept applies to American-style options as well, after adjusting for dividends and interest rates.  Dividends increase put values and decrease call values.  If the dividend is increased, the puts expiring after the ex-dividend date will rise in value while the calls will decrease by a similar amount.  Changes in interest rates have the opposite effects on put and call values.  Rising interest rates increase call values and decrease put values. 

So what happens if the puts and calls for an asset are not in parity?  There are a number of strategies used for option arbitrage.  The most common are the conversion and reverse conversion.  With the conversion you have a long position in the underlying, and simultaneously buy a put and sell a call (at the same strike price).  For a reverse conversion (often called a reversal) you short the underlying while simultaneously selling a put and buying a call.  The figure below shows a conversion in Silicon Labs:

This trade illustrates the basis of arbitrage – buy low and sell high for a small but fixed profit.  Notice that the risk graph for this trade at expiration is a horizontal line.  No matter where the price of the stock goes, you make $460.  The widow of opportunity for these trades usually lasts for only a short time, are really for market makers or floor traders.  They would be able to do the transaction in seconds, and with very low commissions.

But while arbitrage strategies are not very useful for the average trader, the information is worth knowing as a tool for understanding options a little better.  With these types of strategies you can see how puts, calls, and the underlying are interrelated, and get a feel for how options are priced.  You can see how the price of one can’t move very far without the price of the others also adjusting.

If you are familiar with the risk graphs of various trading positions, you know that the risk profiles of all the basic strategies can be duplicated with more complex strategies. 

Consider the simplest option strategy, the long call.  When you buy a call, your loss is limited to the premium paid, while your possible gain is unlimited.  Now consider the purchase of a put and its underlying stock.  Again, your loss is limited to the premium paid for the put plus any out-of-the-money amount, and your profit potential is unlimited as the stock price increases.  Below is a graph comparing these two positions:

If the two graphs appear identical, it’s because they are.  A long put/long stock position is almost identical to owning the call of the same strike and month.  The long put/long stock position is often called a “synthetic” long call.  In fact, the only difference between the two lines is the $8 in dividends the owner of the stock receives.

All basic option strategies have a synthetic equivalent.  The rule for synthetics is that the strikes and months of the calls and puts must be identical.  For all synthetics that involve both stock and options, the number of shares represented by the options must be equal to the number of shares of stock.  Here is a table that lists all the basic synthetics and their equivalents:

Conversion and reverse conversion strategies utilise synthetic strategies.  Looking at the various positions and their equivalent synthetics, if the risks and rewards are the same (across the same strike prices) then a synthetic position should be priced the same as the actual position.  That is, at the same strike prices, a synthetic call should cost the same as an actual call.

Put/Call parity provides one of the foundations for option pricing, and can differ only by trivial amounts such as trading costs.  If the parity is violated, an opportunity for arbitrage exists.  While you may never get the chance to execute an arbitrage trade, it is important to understand them, and how there importance in options pricing.  The other advantage of knowing synthetic relationships is that they can provide you with trading alternatives if the conditions favor them.