What is 'PutCall Parity'
Putcall parity is aÂ principle that defines the relationship between the price of European put options and European call options of the same class, that is, with the same underlying asset, strike price and expiration date. Putcall parity states that simultaneously holding a short European put and long European call of the same class will deliver the same return as holding one forward contract on the same underlying asset, with the same expiration and a forward price equal to the option's strike price. If the prices of the put and call options diverge so that this relationship does not hold, an arbitrage opportunity exists, meaning that sophisticated traders can earn a theoretically riskfree profit. Such opportunities are uncommon and shortlived in liquid markets.
The equation expressing putcall parity is:
C + PV(x) = P + S
where:
C = price of the European call option
PV(x) = the present value of the strike price (x), discountedÂ from the value on the expiration date at the riskfree rate
P = price of the European put
S = spot price, theÂ current market value of the underlying asset
BREAKING DOWN 'PutCall Parity'
Putcall parity applies only to European options, which can only be exercised on the expiration date, and not American ones, which can be exercised before.Â
Say that you purchase a European call option for TCKR stock. The expiration date is one year from now, the strike price is $15, and purchasing the call costs you $5. This contract gives you the rightâ€”but not the obligationâ€”to purchase TCKR stock on the expiration date for $15, whatever the market price might be. If one year from now, TCKR is trading at $10, you will not exercise the option. If, on the other hand, TCKR is trading at $20 per share, you will exercise the option, buy TCKR at $15 and break even, since you paid $5 for the option initially. Any amount TCKR goes above $20 is pure profit, assuming zero transaction fees.Â
Say you also sell (or "write" or "short") a European put option for TCKR stock. The expiration date, strike price and cost of the option are the same. You receive the $5 price of the option, rather than paying it, and it is not up to you to exercise or not exercise the option, since you don't own it. The buyer has purchased the right, but not the obligation, to sell you TCKR stock at the strike price; you are obligated to take that deal, whatever TCKR's market share price. So if TCKR trades at $10 a year from now, the buyer will sell you the stock at $15, and you will both break even: you already made $5 from selling the put, making up your shortfall, while they already spent $5 to buy it, eating up their gain. If TCKR trades at $15 or above, you have made $5 and only $5, since the other party will not exercise the option. If TCKR trades below $10, you will lose moneyâ€”up to $10, if TCKR goes to zero.
The profit or loss on these positions for different TCKR stock prices is graphed below. Notice that if you add the profit or loss on the long call to that of the short put, you make or lose exactly what you would have if you had simply signed a forward contract for TCKR stock at $15, expiring in one year. If shares are going for less than $15, you lose money. If they are going for more, you gain. Again, this scenario ignores all transaction fees.
Put Another Way
Another way to imagine putcall parity is to compare the performance of a protective put and a fiduciary call of the same class. A protective put is a long stock position combined with a long put, which acts to limit the downside of holding the stock. A fiduciary call is a long call combined with cash equal to the present value (adjusted for the discount rate) of the strike price; this ensures the investor has enough cash to exercise the option on the expiration date. Before we said that TCKR puts and calls with a strike price of $15 expiring in one year both traded at $5, but let's assume for a second that they trade for free:
PutCall Parity And Arbitrage
In the two graphs above, theÂ yaxis represents the value of the portfolio, not the profit or loss, because we're assuming that traders are giving options away. They are not, however, and the prices of European put and call options are ultimately governed by putcall parity. In a theoretical, perfectly efficient market, the prices for European put and call options would be governed by the equation:
C + PV(x) = P + S
Let's say that the riskfree rate is 4% and that TCKR stock is currently trading at $10. Let's continue to ignore transaction fees and assume that TCKR doesn't pay a dividend. For TCKR options expiring in one year with a strike price of $15 we have:
C + (15 Ã· 1.04) = P + 10
4.42 = P  C
In this hypothetical market, TCKR puts should be trading at a $4.42 premium to their corresponding calls. This makes intuitive sense: with TCKR trading at just 67% of the strike price, the bullish call seems to have the longer odds. Let's say this is not the case, though: for whatever reason, the puts are trading at $12, the calls at $7.
7 + 14.42 < 12 + 10
21.42 fiduciary call < 22 protected put
When one side of the putcall parity equation is greater than the other, this representsÂ an arbitrage opportunity. You can "sell" the more expensive side of the equation and buy the cheaper side to make, for all intents and purposes, a riskfree profit. In practice, this means selling a put, shorting the stock, buying a call and buying the riskfree asset (TIPS, for example).
In reality, opportunities for arbitrage are shortlived and difficult to find. In addition, the margins they offer may be so thin that an enormous amount of capital is required to take advantage of them.

Put On A Call
One of the four types of compound options, this is a "put" option ... 
Call On A Call
A type of compound option in which the investor has the right ... 
Bear Call Spread
A type of options strategy used when a decline in the price of ... 
Expiration Date (Derivatives)
The last day that an options or futures contract is valid. When ... 
Early Exercise
The exercise of an option prior to its expiration date. Early ... 
Leg
A leg is one component of a derivatives trading strategy, in ...

Options & Futures
What is PutCall Parity?
Putcall parity describes the relationship that must exist between European put and call options with the same expiration date and strike prices. 
Options & Futures
PutCall Parity And Arbitrage Opportunity
Look at trades that are profitable when the value of corresponding puts and calls diverge. 
Options & Futures
Three Ways to Profit Using Put Options
A brief overview of how to profit from using put options in your portfolio. 
Options & Futures
The Basics of Options Profitability
The adage "know thyself"and thy risk tolerance, thy underlying, and thy marketsapplies to options trading if you want it to do it profitably. 
Options & Futures
Getting Acquainted With Options Trading
Learn more about stock options, including some basic terminology and the source of profits. 
Options & Futures
Options Basics: What Are Options?
An option is a contract that gives the buyer the right, but not the obligation, to buy or sell an underlying asset at a specific price on or before a certain date. An option, just like a stock ... 
Options & Futures
Going Long On Calls
Learn how to buy calls and then sell or exercise them to earn a profit. 
Options & Futures
Exploring European Options
The ability to exercise only on the expiration date is what sets these options apart. 
Options & Futures
Forecasting Market Direction With Put/Call Ratios
Options are not only trading instruments but also predictive tools that can help us gauge the feelings of traders. 
Stock Analysis
Profit With Less Risk With This Options Strategy
Capital preservation and minimizing losses should be the most important objectives of any investor or trader. Warren Buffett is credited with the saying: Rule No. 1: Never lose money Rule No. ...

How are call options priced?
Learn how aspects of an underlying security such as stock price and potential for fluctuations in that price, affect the ... Read Answer >> 
How do I change my strike price once the trade has been placed already?
Learn how the strike prices for call and put options work, and understand how different types of options can be exercised ... Read Answer >> 
How do I set a strike price for an option?
Learn about the strike price of an option and how to set a strike price for call and put options depending on risk tolerance ... Read Answer >> 
When holding an option through expiration date, are you automatically paid any profits, ...
Holding an option through the expiration date without selling does not automatically guarantee you profits, but it might ... Read Answer >> 
What happens when a security reaches its strike price?
Learn more about the moneyness of stock options and what happens when the underlying security's price reaches the option ... Read Answer >> 
When is a call option considered to be "in the money"?
Learn about call options, their intrinsic values and why a call option is in the money when the underlying stock price is ... Read Answer >>