What is a put-call parity?

It doesn’t matter if you are a stock trader, bond trader, or forex trader; your ultimate goal is to earn more money with minimum risk. One of the most critical principles options traders need to understand is the put-call parity.

This article focuses on the skeleton of this concept. First, let’s cover the basics of what options are, how they work and what is involved.

A general overview of options

Options are contracts that grant holders the right (but not obligation) to buy or sell underlying securities like stock at a specific price within a defined period and before a particular expiration date.

In the event a holder fails to exercise the option before the expiration date, they can no longer use it, and the option loses its value. Usually, option contracts control 100 shares of an underlying stock.

Here are two types of options:

Call option

Call options offer holders the right to buy underlying securities at a predetermined price only during a designated period. Call buyers are frequently optimistic, so they purchase calls to make money from an expected upside move.

Put option

Put options provide holders with the right, not the obligation, to sell underlying securities at a decided price by a specified date. Usually, one buys a put when they are unsure about the market and a stock’s potential.

A predetermined price is referred to as the strike price since a trader often strikes when the security price drops to that value or lower.

What is a Put-call parity?

The Put-call parity principle dictates that option trading positions within similar payoff profiles are obligated to arrive with the same loss or profit at expiration. This makes it so that no arbitrage opportunity exists.

The put-call parity principle asserts that holding a “short European style” put option is equal to having a “long European style” call option. It delivers the same return as a single forward contract by the same means with the exact same expiration, including a forward price that’s equal to the option’s strike price.

More simply stated: buying a put and a call with the same expiration date and the same strike price has the same value as the stock price less the strike price.

For the put-call parity principle to continue, these conditions must be present:

  • Both call and put options must have an equal strike price
  • The options must be of European style
  • No exchange or brokerage fees
  • The stock should not pay dividends
  • Interest rates need to remain constant until the expiration date

In 1969 by Hans R. Stoll first identified the Put-call parity concept. This principle gets support based on the argument that an arbitrage opportunity would materialize if there exists a variance between put and call values. Arbitrage traders can pocket risk-free returns until the put-call parity becomes restored.

Arbitrage Strategy

Arbitrage is an approach to exploiting price variances in an assent within different markets. To illustrate this, say an individual has stock in Company AB, trading $40 on Nasdaq. Simultaneously, the AB stock listed on the London Stock Exchange is trading at $35. Any trader can easily purchase the stock on the London Stock Exchange for $35 and sell it on the Nasdaq for $40. This allows him to gain a profit of $5 per share.

The formula for Put-call parity

Here are the critical components of the put-call parity formula:

Sell Put Option

Buy Call Option

= Long Stock

The put-call parity formula is: Call – Put = Stock – Strike.

Let’s say stock XYZ was trading at $40, and the option strike prices were $35. The call option premium would be $8, while the put option is $3. Putting the put-call parity into action looks like (8 – 3 = 40 – 35).

Now, say you are short a put and long a call at the same strike price, then in the same expiration month, you are effectively long the underlying shares at the strike price level.

This equation allows you to add or subtract components from one side to the other so you can create payoffs from different option strategies.

For instance, say you move the call to the other side of the equation (add it to both sides and subtract the stock leg from both ends). It should look like this: P – C = S

Put-call parity significance:

Put-call parity normally works well with European-style options, but U.S. market makers also use it to keep prices level for all American-style options.

This concept applies to many different types of financial securities as a means of gauging the estimated value of a put or a call respective to the other components.

Putting it all together:

The put-call parity principle directly defines the relationship between a call, a put, the stock, and strike price. When you understand this principle well, you can discern how option prices are impacted by supply and demand.

This gives you a better grasp on how option values in the same financial security are related and a better understanding of the mechanics that smart investors use to value options.

Your ability to distinguish market price differences or divergence before others notice helps you become a more successful trader. To be a profitable options trader, you have to put in the effort, time, and study to learn essential principles like the put-call parity.