In trading traditional options there is a concept known as put/call parity, which says that a call option at one strike price and expiry will have a corresponding relationship with the put of the same strike price and expiry, and vice versa.  It is this corresponding value that makes call put arbitrage possible.  IN cases where thee prices diverge, a put call arbitrage can be accomplished in which the trader makes a small profit from the price differential with little or no risk.  The arbitrageurs can continue to step in and take these profits until put/call parity is restored.  While it is unlikely that an individual trader will ever take advantage of this type of put call arbitrage (the price discrepancies typically last just moments), it is useful to understand the theory behind the strategy, and gain a deeper understanding of the relationship between puts, calls and the underlying stocks.

Conversion and Reversal Arbitrage

Conversion and reversal arbitrage are some of the most common put call arbitrage strategies.  These use synthetic positions in which the risks and rewards are the same as if the positions were undertaken on their own.

A conversion is done by purchasing the actual stock shares and then simultaneously selling a call option and buying a put option.  The reverse conversion works the same, but the stock is shorted while a call is bought and a put is sold.  In the case of the conversion a synthetic short position is created, while in the case of the reversal a synthetic long position is created.

These synthetic positions are actually the same as buying or shorting the underlying stock, assuming the strike price and expiry of the calls and puts are the same.  The trades guarantee a profit in cases where put/call parity is out of whack.

This trade illustrates the basics of put call arbitrage, in which a trader can make a small and nearly guaranteed profit with little or no risk.  The profit is generated by the difference in price between the call and put, so once the trade is placed it makes no difference what occurs with the price of the underlying stock.  As you might guess, because these trades are akin to free money, they occur very rarely in practice.  When they do occur, the window of opportunity is quite short, with market makers typically stepping in immediately and placing the transactions that restore put/call parity.

In Conclusion

The concept of put/call parity is one of the foundations in options pricing, and shows us how the price of a call option cannot move far without having an impact on the price of the corresponding put option.  Any situation in which parity is violated creates an opportunity for put call arbitrage, though these opportunities are almost always very short lived.  While you might not be able to profit directly from synthetic strategies such as the conversion and reversal trade, it can help to know about these as they give you deeper knowledge into how options work.