#### Options Idea

Put-Call Parity & Option Pricing
Specialty: OPTIONS
Published: 2/1/2013

#### More from Alan Ellman

This article has a few advanced concepts that I hope you find interesting but is not necessary to master or memorize, writes Alan Ellman of TheBlueCollarInvestor.com. Some of the material may make your head spin a bit as it did mine as I was writing the article!

Definition and Example
Put call parity is an option pricing concept that requires the time (extrinsic) values of call and put options to be in equilibrium so as to prevent arbitrage (Arbitrage is the simultaneous purchase and sale of an asset in order to profit from a difference in the price).

It is when the value of a call option, at one strike price, implies a certain fair value for the corresponding put, and vice versa. The argument, for this pricing relationship, relies on the arbitrage opportunity that results if there is difference between the value of calls and puts with the same strike price and expiration date. Arbitrageurs would step in to make profitable, risk-free trades until the departure from put-call parity is eliminated. This relationship is strictly for European-style options, but the concept also applies to American-style options, adjusting for dividends and interest rates. If the dividend increases, 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. Rising interest rates increase call values and decrease put values.

Put-call parity graph
Click to Enlarge

The above chart depicts a put-call parity relationship. We see that a long-stock/long-put position (red line) has the same risk/return profile as a long call (blue line) with the same expiration and strike price. The only difference between the two lines is the assumed dividend that is paid during the time to expiration. The owner of the stock (red line) would receive the additional amount, while the owner of the call (blue line) would not. However, if we assume no dividend would be paid to stockholders during the holding period, then both lines would overlap. From this chart one can see that if you sold a cash-secured put instead of writing a covered call, the put-call parity concept would account for that dividend difference.

Click to Enlarge

When you buy a call, your loss is limited to the premium paid while the possible gain is unlimited. Now, consider the simultaneous purchase of a long put and 100 shares of the underlying stock. Once again, your loss is limited to the premium paid for the put, and your profit potential is unlimited if the stock price goes up.

Put Call Parity: An Example

Assumptions:
\$50 call = \$2
\$50 put = \$2
At expiration BCI still trading @ \$50

Buy 1 x \$50 call for \$200
Buy 100 x BCI and 1 x \$50 put for \$700

Results:
Calls expire worthless = \$200 loss
Puts expire worthless, no loss or gain on shares = \$200 loss

Since put call parity exists, the net losses on both positions are exactly the same so that there are no arbitrage opportunity to be exploited by being long one position and shorting the other simultaneously.

NEXT PAGE: Put-Call Parity Rules

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