How are puts and calls secretly connected?
Our guide will discuss the relationship in detail as we delve into the “put-call parity” principle and its formula. However, an understanding of this concept can greatly assist market makers in preventing arbitrage and maintaining a fair and efficient options market. On the other hand, traders can apply the same principle and formula to create synthetic positions, construct hedging strategies, and identify arbitrage opportunities.
We’d encourage anyone who is a new or intermediate options trader to read this guide in its entirety to get familiar with the put-call parity formula and how it can work to your advantage. In this guide, we will break down the formula, explain its meaning, and demonstrate its application in real trading.
What Is Put-Call Parity? (In Plain English)
Put-call parity is a fundamental financial principle that defines a specific relationship between the price of a call, a put, and the underlying stock. What this principle states is that the cost of a call option, along with the strike price’s present value, is equal to the price of a put option, along with the price of the underlying asset. This refers specifically to European options, which can only be exercised on their expiration date (and not before).
Real-World Analogy: Put-call parity can best be described with the analogy of a seesaw balancing two sides of a bet.
Why does the put-call parity even exist in the first place? For one thing, it helps with the determination of fair prices for options, which can ultimately prevent arbitrage opportunities (free money from price inefficiencies). When the put-call parity is violated, it could indicate a potential arbitrage opportunity. On the one hand, it can be utilized by trading apps to prevent arbitrage opportunities in the first place and make their markets more efficient. On the other hand, it can also be used by investors to spot arbitrage opportunities, even if they’re short-lived and/or small.
The Put-Call Parity Formula (And What It Really Means)
The idea behind put-call parity is that an investor’s portfolio consists of a long call option and a short put option that are equal to another contract on the same underlying asset, which also features the same strike prices and expiration date. The long call and short put also have the same expiration date and strike prices.
The Formula
C + PV(K) = P + S
What do all these symbols mean? This should make it much clearer.
- C = Call price
- PV(K) = Present value of strike price (discounted from the future)
- P = Put price
- S = Stock price
Adding the call price to the present value of the strike price should equal the put price plus the stock price. This forms the basis of the parity principle, in which the two sides of the equation must match to avoid arbitrage. This stems from a desire for markets to be more efficient in valuing certain assets and securities. Achieving parity, in this case, means that there will be few, if any, arbitrage opportunities or moments when traders can take advantage of inefficiencies in the numbers.
Visual Example: Breaking Down a Put-Call Parity Trade
Let’s examine the put-call parity formula to gain insight into how this might play out in the real world, using some hypothetical numbers as an example. In this scenario, we will present the numbers for the formula, walk you through both sides of the equation, and demonstrate how it all balances out. We will even outline what happens if the equation doesn’t balance out and what that means for the trader.
Let’s examine the hypothetical scenario below, assuming it’s a 1-year option with a risk-free rate of 5%.
- Stock price = $100
- Strike price = $100
- Call = $7
- Put = $5
Now, let’s plug these numbers into the put-call parity formula.
C + PV(K) = P + S —> $100 + $7 = $5 + $100
As you can see, there is a discrepancy of $2 between the two sides of the equation, which presents a good arbitrage opportunity for traders, as the equation isn’t perfectly balanced. The put price should be $7 instead of $5 if the markets are more efficient. When the market price is slightly different, as is the case here, it can indicate an arbitrage opportunity for traders who want to capitalize on small discrepancies.
Why Does Put-Call Parity Matter for Options Traders?
What is the significance of the put-call parity principles for stock option traders online? We’ve outlined below a few reasons why traders and market makers utilize the put-call parity to their advantage when setting prices and seeking the best trade opportunities, respectively.
- It reveals fair pricing between put and call options. From the standpoint of market makers, this helps make the markets as efficient as possible and avoid price discrepancies that lead to arbitrage opportunities.
- From the viewpoint of the options trader, it can help you spot mispriced options so you can take advantage of arbitrage opportunities. Mispricings in the markets can increase the trader’s profit margin and ultimate profit potential.
- The put-call parity can help traders understand synthetic positions (e.g., synthetic long stock) by revealing how a combination of options can replicate the payoff of another options contract.
- From a trader’s perspective, put-call parity can be used to build the foundation for advanced strategies, such as box spreads and conversions.
Common Misconceptions about Put-Call Parity
Let’s address some of the mistakes that traders make in how they view the put-call parity and its use in their trading sessions. You don’t want to get these ideas wrong because you could miss out on a lot of the opportunities that come with the put-call parity formula and principles. This section will clarify many common misconceptions and set the record straight.
“It only works for European-style options.”
While the put-call parity exists primarily as a tool for European-style options, it can be technically applied to American options, though it’s far less common. American options can be exercised at any point before the expiration date; however, using the put-call parity formula can be more complex due to factors such as early exercise and dividends. The relationship between the prices of calls and puts with American options isn’t as straightforward as it is with European options.
“It only applies at expiration.”
The put-call parity principle provides insights into option prices before expiration and for American options, as previously discussed in the last point. Put-call parity can provide a benchmark for pricing European options before their expiration, though the put-call parity is exact at expiration. While it’s true that parity only applies at expiration, it’s precisely at that time when the relationship between the calls and puts is most precise.
“Put-call parity is theoretical only.”
Nothing could be further from the truth because the formula and principle can be used in real life by arbitrageurs who are looking for imbalances in the equation to find places where the market makers have mispriced stocks, assets, or other securities. Taking advantage of these discrepancies can help traders increase their overall profit potential, and over time, this can equate to substantial profits.
Put-Call Parity in Action: Practical Uses for Traders
We’ve touched on a few of the ways traders can take advantage of the put-call parity, but we’d like to discuss it in more detail to gain a better understanding of the practical applications of these principles and help options traders get ahead.
- Exploit Violations—When arbitrage traders identify instances where the same asset or similar assets with identical cash flows are trading at different prices, they can exploit these discrepancies to pursue larger profits. Traders can examine stocks on other exchanges or even find differing prices for commodities in various locations to take advantage of these mispricings.
- Verify if an Option is Overpriced or Underpriced—Arbitrage traders can simultaneously buy the asset in the market where it is priced lower and sell it in the market where it’s priced higher. Significant differences from the parity formula can indicate market inefficiencies, which can help traders make more informed decisions about buying or selling options once they know whether they’re overpriced or underpriced.
- Create Synthetic Positions—When liquidity is low in a specific option, traders can create synthetic positions that replicate the payoff of one type of option using a combination of other options or the underlying asset. Creating these positions involves leveraging the relationship between call and put options with the same strike prices and expiration dates.
Quick Recap: What You Should Know Now
If you’ve learned nothing else from our guide on the put-call parity, we’d like you to take away the following three points before working the formula and principle into your trading routine:
- Put-call parity links, puts, calls, and the underlying stock.
- The formula helps ensure pricing is fair and balanced.
- Smart traders utilize it to identify mispriced opportunities or construct synthetic trades.
Final Thoughts on Put-Call Parity
Suppose you’re learning about put-call parity for the first time and are unfamiliar with the principle. In that case, we encourage you to begin with paper trading or a demo account to test the formula and see if it can help identify arbitrage opportunities. Once you’ve gained some experience and confidence with time, you can begin with smaller trades or investments to keep the potential losses to a minimum until you learn to use the put-call parity principle effectively.
It’s also key to take action with your new knowledge, so we encourage traders new to using put-call parity to compare the real markets to the formula. A good way to practice this reward is to build synthetic positions to gain some additional experience. Ultimately, understanding the parity formula helps traders to avoid mistakes and spot better trades.
