Warrior Trading Blog

Put-Call Parity Explained in Depth

Put Call Parity

Whether you are a stock trader, a bond trader, or a forex trader, your ultimate goal is to earn money with minimum risk. For options traders, one of the most important principles you need to understand is the put call parity.

In this article, we will be focusing on the nuts and bolts of this concept. But before we do that, it is important to get a basic of understanding what options are, how they work and what is involved.

What are options?

An option is a contract that gives its holder the right, but not the obligation, to buy or sell an underlying security such as a stock, at a specific price within a certain period of time or by an expiration date.

If the holder fails to exercise the option by its expiration date, they can no longer do so and the option becomes valueless. Typically, each options contract controls 100 shares of an underlying stock.

There are two types of options:

  • Call option

A call option gives its holder the right to buy an underlying security at a predetermined price at a stipulated period of time.

Call buyers are generally bullish, so they purchase calls to try and make money from an expected upside move.

  • Put option

A put option gives its holder the right (but not the obligation) to sell an underlying security at a predetermined price by a set date. Typically, you buy puts when you are bearish about the direction of the market and/or a stock’s potential.

The predetermined price is known as the strike price since a trader will presumably strike when the price of the security drops to that value or lower.

Put-call parity

Put call parity principle requires that option trading positions with similar risk or payoff profiles must end up with the same loss or profit upon expiration so that no arbitrage opportunity exists.

This principle states that holding a short European style put option is the same as holding a long European style call option, delivering the same return as a single forward contract on the same instrument with the same expiration with a forward price equal to the option’s strike price.

In other words, buying a put and a call with the same expiration date and the same strike price will have the same value as the stock price less the strike price.

For the put call parity principle to hold true, the following conditions must be present:

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

Put call parity concept was first identified in 1969 by Hans R. Stoll. Support for this principle is based upon the argument that an arbitrage opportunity would materialize if there is a variance between put and call values. Arbitrage traders would come in to pocket risk-free returns until the put-call parity is restored.

Arbitrage

Arbitrage is the strategy of exploiting price variances in an assent in different markets.

For example, let us say an individual owns stock in Company XY, trading at $50 on the Nasdaq. At the same time, the XY stock listed on the London Stock Exchange trades at $47. A trader could purchase the stock on the London Stock Exchange for $47 and sell it on the Nasdaq for $50. This would earn him a profit of $3 per share.

Put-call parity formula

The key components of the put call parity formula are:

  • Sell Put Option
  • Buy Call Option
  • Equals Long Stock

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

Assume stock ABC was trading at $40 and the option strike prices were $35. The premium for the call option would be $8 while the put option is $3. This is the put-call parity in action as (8 – 3 = 40 – 35).

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

You can use this equation to add or subtract components from one side to another to create payoffs of other option strategies.

For example, if you move the call to the other side of the equation by adding it to both sides and minus the stock leg from both ends, that will give you this:

P – C = S

Significance of put call parity

Although put call parity generally works well with European-style options, it is also used by market makers in the United States to keep prices in line for all American-style options.

In addition, this concept is used for many different types of financial securities as a means of gauging an approximate value of a put or a call relative to its other components.

Final Thoughts

Put call parity principle simply defines the relationship between a call, a put, the stock and strike price. By understanding this principle, you can begin to better comprehend how option prices are impacted by demand and supply.

You will also get to grasp how all option values on the same underlying financial security are related as well as some mechanics that savvy investors may use to value options.

Remember that the ability to spot market mispricing or divergence before others is what makes one a successful trader. Becoming a profitable options trader requires effort, time and learning certain principles including the put call parity.

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