What Is Put-Call Parity? Discover The Formula That Keeps Options Trading Fair

Jeremy BiberdorfBy: Jeremy Biberdorf

July 8, 2024July 8, 2024

Put-call parity is like the scales of justice for options trading. It’s a crucial financial principle that explains how the prices of call options and put options are linked when they share the same strike price, expiration date, and underlying asset. This rule only applies to European options, which can’t be exercised until their expiration date.

The idea has been around since the medieval times, but it was really pinned down early in the 20th century. Understanding put-call parity helps traders ensure that the pricing of options stays consistent, preventing anyone from getting an unfair edge through arbitrage.

As I dive deeper, you’ll see just how this concept helps to stabilize and predict movements in the options market. Stick with me, and I’ll show you how mastering put-call parity can significantly benefit your trading strategy. If you prefer learning by video, check out the video below:

Key Takeaways

  • Put-call parity is a fundamental concept in options trading that links the prices of European call and put options with the same strike price and expiration date, ensuring no arbitrage opportunities.
  • Arbitrage opportunities are rare in real-world trading due to market efficiency, competition, and transaction costs, making mispricings short-lived.
  • Dividends impact put-call parity by affecting stock prices on the ex-dividend date, influencing the value of call and put options differently.
  • Understanding put-call parity is crucial for traders to ensure fair pricing, exploit potential arbitrage opportunities, and make informed trading decisions.

What is Put-Call Parity?

Simply put, put-call parity is a financial principle that states if you have a call option and a put option with the same expiration date and strike price on the same stock, they will end up having the same value as owning a forward contract for that stock at the same strike price.

Put-call parity is an essential principle in the world of European options trading, serving as a fundamental framework that ensures the consistency of option pricing across calls and puts. This principle is particularly relevant for options of the same class, which means they share the same underlying asset, strike price, and expiration date.

Unlike American options, which can be exercised at any time before they expire, European options apply strictly to situations where options can only be exercised at expiration. This restriction simplifies the relationship and calculations, ensuring that the options behave predictably in line with the underlying theory.

In practical terms, this means if you’re looking at European options with identical strike prices and expiration dates, their prices should align in such a way that no arbitrage opportunities exist due to price discrepancies. This alignment helps in maintaining fair pricing in the markets and also assists traders in making informed decisions.

 Put-Call Parity

What is Put-Call Parity Formula?

The concept of put-call parity was first introduced by economist Hans Stoll in his groundbreaking 1969 paper, “The Relation Between Put and Call Prices,” published in the Journal of Finance.

Stoll’s insights into the connection between put and call options established a foundational theory in financial economics and options pricing. His formula demonstrates a mathematical relationship that guarantees no arbitrage opportunities between calls and puts, sharing the same strike price and expiration date.

Here’s how that relationship is expressed as a mathematical formula:



P is the price of the European Put Option.

S is the spot price (current price) of the underlying asset.

C is the price of the European Call Option.

PV(x) is the strike price value, which is discounted from the expiration date’s value.

Why Put-Call Parity is Important and How It Relates to Arbitrage Opportunities

Put-call parity is crucial for several reasons, primarily because it helps ensure that the pricing of options remains consistent and fair, preventing the possibility of arbitrage opportunities. Arbitrage involves simultaneous buying and selling of securities in different markets or forms to take advantage of differing prices for the same asset.

In the context of put-call parity, if the relationship outlined by the parity equation is not held due to mispricing between the call and put options with the same strike price and expiration, an arbitrage opportunity exists. Savvy traders can exploit this discrepancy to make a risk-free profit.

How Common Are Put-Call Arbitrage Opportunities in Real-World Trading?

While the example above illustrates how arbitrage might work theoretically, such opportunities are relatively rare in real-world markets, particularly in highly liquid markets where options like those on major stocks or indices are traded. This is because:

  • Market Efficiency: Financial markets, especially those in developed economies, tend to be highly efficient. Prices adjust very quickly to new information, so any mispricing is typically corrected swiftly.
  • High Competition: Many traders and sophisticated algorithms are continuously scanning for arbitrage opportunities. When one arises, it is quickly exploited, closing the gap almost as soon as it appears.
  • Transaction Costs: Even when slight mispricings are found, transaction costs, including fees and the bid-ask spread, can often offset the potential profits from arbitrage.

How Dividends Affect Put-Call Parity

When dealing with options trading, it’s a must to factor in dividends, especially when dealing with put-call parity. This concept assumes no dividends are paid; however, the real-world often presents a different scenario, where dividends can significantly influence option prices.

If the underlying stock pays dividends, the equation must account for this. Dividends tend to decrease the stock price on the ex-dividend date, which impacts call and put prices differently.

Implications for Traders:

  1. Call Options: The value of call options may drop as the ex-dividend date approaches because the stock price is expected to decrease by the dividend amount, making these options less appealing.
  2. Put Options: Conversely, put options might gain in value around the ex-dividend date. The expected drop in stock price increases the likelihood that the put will be in-the-money, and more valuable.

Put-Call Parity: My Final Thoughts

Understanding what is put-call parity and its implications in options trading is crucial for anyone looking to dive into this aspect of the financial markets. This principle not only ensures fair price relationships among options but also serves as a critical check against potential arbitrage opportunities that could skew market efficiency.

As we’ve explored in this article, put-call parity acts like a balancing scale, ensuring that the prices of call and put options, when adjusted for the present value of exercise prices and any dividends, align to prevent free money opportunities through arbitrage.

While true arbitrage opportunities are rare due to market efficiency and the quick actions of other traders, knowing how to identify and understand these situations is invaluable.

For those looking to expand their knowledge on the dynamics of options trading, exploring topics I have covered like what is a good implied volatility for options and option volatility and pricing strategies can provide deeper insights and aid in your forming a well rounded perspective into options. These articles will equip you with the necessary tools to interpret volatility levels and apply complex pricing models effectively.

As you continue your journey in options trading, remember that mastering concepts like put-call parity is foundational. It not only aids in making informed trading decisions but also sharpens your ability to foresee and react to market movements and pricing inefficiencies. So, keep learning and stay vigilant in applying these principles to your trading strategy.

Jeremy Biberdorf
Jeremy Biberdorf

About the Author:

Jeremy Biberdorf is the founder of Modest Money. He's a father of 2 beautiful girls, a dog owner, a long-time online entrepreneur and an investing enthusiast.

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