Demystifying Options: Explaining Put/Call Parity - Part Two

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...continued from Part One

An Arbitrage Opportunity
ìFine,î you might say ìthatís the theory, but is it the way options really trade?î

The answer is ìyes.î The reason is that when call or put time premiums get out of line with each other, option market makers can make a risk-free arbitrage profit.

Let us look at the simplest arbitrage. Suppose that the time premium of a particular put is greater than the time premium of the corresponding call (same stock, strike and expiration).

Here the market maker can take advantage of the difference in the time premiums by writing the put and buying the call. What the market maker has done is to create a ìsyntheticî long stock position with a free credit of premium. The market maker can fully offset his risk by selling the stock. The net credit of time premium from this transaction will be his arbitrage profit.


From the above, you get the first put/ call parity rule: If you buy a call and sell a put at the same strike price and expiration, you get the equivalent of a long stock position. Or,

• Rule 1: (+) Buy Call & (-) Write Put = (+) Buy Stock

From the aforementioned, it follows that if you write a call and buy a put at the same strike price, you get the equivalent of a short stock position.

• Rule 2: (-) Write Call & (+) Buy Put = (-) Short Stock

The other put call parity rules come from the fact that option time premiums are essentially the same for calls and puts at the same strike price.

• Rule 3: (+) Buy Stock & (+) Buy Put = (+) Buy Call

• Rule 4: (-) Short Stock & (-) Write Put = (-) Write Call

• Rule 5: (-) Short Stock & (+) Buy Call = (+) Buy Put

• Rule 6: (+) Buy Stock & (-) Write Call = (+) Write Put = Covered Call

Notice that if you move any of these transactions to the other side of the equal sign, you change the strategy from a short to a long (or vice versa) and (remembering your algebra) the ì+î sign to a ì-î sign (or vice versa).

Uses of Put/Call Parity
Can I take advantage of the put/call parity rules?

Because the market maker has a clear advantage in trading options, it is unlikely that the typical investor will see actual ìrisk-freeî arbitrage opportunities from put/call parity. However, these rules are useful, because knowing them can help you quickly determine what your strategy alternatives are. Here are some applications

• Rule 3: Often, you may be interested in buying a particular stock, but you are concerned about the risk and may want to hedge it with a put. Knowing rule number 3 tells you that buying the call will give you the same risk/reward as buying the stock and the put.

• Rule 6: Often, you may see attractive covered call opportunities, where the call is in-the-money. Here you may be reluctant to establish the position in fear of having the call exercised. Here you can write a cash covered put instead of the covered call. (In an earlier example, we showed a comparison between an in-the-money covered call (the November $22.50 call) and the corresponding out of-the-money put write (also November $22.50 strike) on Internet Security (ISSX) with the stock at $23.21. Although the cash covered put offered a somewhat lower per annum yield than the covered call (51.0% versus 57%), it also offered investors the advantage of no closing transactions if the stock ends up above the $22.50 strike price.)
  

Posted By: Value Line"

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