Put Call Parity

"Put-call parity" - a strange term for a logical phenomenon. The put-call parity can clarify the option pricing process and help keep call and put prices "in-line."

Ever wonder how options are priced, especially on days when market conditions are changing rapidly and sometimes drastically? Many investors make the mistaken assumption that option prices are made simply at random, at the whim of some market professional or "big market player." In fact, there's a measurable relationship between the price of a call and put with the same month/strike price and the current price of the underlying stock. It overlays a method on the option pricing process and is called put-call parity.

There"s an option strategy called a "combination" (or "combo"), a generic term that refers to buying and/or selling a call and put on the same underlying stock in a variety of ways. Very commonly, however, this term refers specifically to a position that involves either buying a call and selling a put (both long positions) or selling a call and buying a put (both short positions) with the same underlying stock, strike price, and expiration month. These strategies are the very basis of put-call parity.

This combination requires selling a call and buying a put with the same strike price, expiration month, and underlying stock. It"s also referred to as a "short stock combo" because you end up with an option position that has profit and loss characteristics similar to a short position in the underlying stock. With both you may profit if the stock goes down and lose money if the stock goes up.

Because of the similarity in P&L profiles between the two positions the short stock combo is also referred to as "synthetic short stock." The logic behind put-call parity is that the price you receive for this synthetic short stock may reflect the price that you would pay for the underlying stock itself. Let's consider an example of selling a combo and buying shares of underlying stock with market prices of each in proper alignment.

• You"re assigned on short XYZ 60 call - sell 100 XYZ at $60 per share
• Long put expires out-of-the-money and worthless

You lose $1 per share on your stock for a net loss of $100, but you took in a $180 net credit. Your net profit = $80.

If XYZ stock exactly at 60:

• Call and put expire at-the-money and worthless

You keep stock at a loss $1 per share for a net loss of $100, but you took in a $180 net credit. Your net profit = $80

• You exercise your XYZ 60 put - sell 100 XYZ at $60 per share
• Short call expires out-of-the-money and worthless

You lose $1 per share on your stock for a net loss of $100, but you took in a $180 net credit. Your net profit = $80

So, if you sold the combo and bought 100 shares XYZ stock at the prices stated in our example, you"d make a profit of $80 no matter where XYZ stock is trading at expiration? Not really. Consider the interest you could have received if the $6,100 stock investment had been working for you elsewhere, like in an interest bearing account. How much would this be? Assuming an interest rate of 5% and about 95 days until expiration, you could have received approximately $80 for this time period – the theoretical maximum profit from the option/stock strategy itself. This position could then be considered a "wash"...i.e., no profit and no loss.

Given the prices we paid/received for the put and call compared to the current price of WMT stock, you could say they were at parity with the stock price. You were able to buy 100 shares of real stock and sell 100 shares of synthetic stock, including the foregone interest, at an equivalent price.

If you could sell the combo in our example for more than a net $180 credit, perhaps by purchasing the put for less and/or selling the call for more, and still purchase 100 shares of stock at $61 per share, you could then lock-in a profit. This would be called arbitrage: the simultaneous purchase and sale of the same commodity in different markets in order to make an immediate riskless profit.

If the prices of puts and calls get "out of line" with each other, and in this case the combo could actually be sold for more, then investors and professional traders may enter the market to do this. The marketplace is not inclined to give away profits in this way so the result is the prices of the 60 call and put requoted at the relationship they should be – in combination at parity with the price of the stock. Together, put-call parity and the possibility of arbitrage keep call and put prices in line, one definition of an "efficient" option marketplace.

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