• Skip to primary navigation
  • Skip to main content
  • Skip to primary sidebar

Epsilon Options

Options Trading Education

  • Home
  • How Options Work
    • In The Money (ITM) Options
    • Puts and Calls Explained
    • Learn Options Trading
    • LEAP Options Explained
    • Put Call Parity
    • Buy to Open vs Buy to Close
    • Out Of The Money (OTM) Options
    • Strike (Exercise) Price
    • Implied Volatility
    • Volatility Skewness | IV Skew In Options
  • Options Greeks
    • Delta
    • Vega
    • Gamma
    • Theta
    • Rho
  • Options Spreads
    • Long Call
    • Long Put
    • Bear Put Spread
    • Iron Condor
    • Bull Call Spread
    • Covered Calls
    • Synthetic Covered Call
    • Buying Straddles Into Earnings
    • Covered Call LEAPs
    • Calendar Spread
    • Backspread
    • Strangle
    • Butterfly
    • Protective Put
    • Long Box Spread
    • Straddle
    • Vertical Spread
    • Zero Cost Collar
  • Options Brokers Reviews
  • Blog
  • Show Search
Hide Search

Put Call Parity

Table of Contents

  • Put Call Parity Introduction
  • Example Of Put Call Parity In Action
    • In a years time:
    • Using a put option:
  • Can Put Call Parity Be Traded?
  • An Illustrated Example Of Put Call Parity

Put Call Parity Introduction

Options trading can be relatively simple and can also become highly technical. One of the most important basic concepts when it comes to trading options is the concept of put call parity.

Put call parity only applies to European options, which unlike American options, can only be exercised on expiration day.

Put call parity is a principle that defines the relationship between calls and puts that have the same underlying instrument, strike price and expiration date.

The idea of put-call parity states that holding a sort 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.

The put-call parity principle can be expressed as the following equation: C+PV(x)=P+S. 


Example Of Put Call Parity In Action

Here is an example of the principle in action:

Suppose that stock ABC is currently trading at $15 per share. An investor decides to purchase European style call option on ABC that expires in one year with a strike price of $15.

The call option gives the investor the right, but not the obligation, to purchase ABC at the strike price of $15 one year from now, regardless of what the stock price is at that time. 


In a years time:

If in a year the stock price is trading at $10 per share, the investor would not exercise his or her right to purchase the shares at $15, as this would automatically create a loss.

In this case, the call option would simply expire worthless, and the investor would lose the entire $5 premium paid for the call. If the price of ABC as moved higher to $20 per share, the investor could exercise the option to purchase shares at $15.

Because the investor paid $5 for the option, this scenario would create a break-even trade. If the stock price is above the break-even point of $20, however, the investor would profit point-for-point as the stock price moves above $20. 


Using a put option:

Now suppose that the investor also writes or sells a put option on ABC with the same expiration date and strike price. The investor also receives the same $5 premium that was paid for the purchase of the call option.

It is up to the put buyer to exercise the option if appropriate at expiration. If the price of ABC declines to $10 at expiration, both the put buyer and seller would break-even.

If the price of ABC declines below $10, the put buyer would make a profit while the put seller would incur a loss.

If the stock price is above $15 at expiration, the seller would keep the entire $5 premium as profit while the buyer would lose the entire $5 premium paid for the put. 

You will notice that if you add the profit ot loss of the call to the profit or loss on the put, it equals the profit or loss that would be incurred by buying a forward contract for the stock at $15. 


Can Put Call Parity Be Traded?

This concept can be traded using a methodology called arbitrage.

This form of trading can be highly sophisticated. Such opportunities rarely exist in liquid markets as they can present a risk-free profit.

Arbitrage using put-call parity would involve the buying and selling of options if the option values were to get out of line, thus disrupting the put-call parity relationship.

Such opportunities are not only rare in modern markets, but also close quickly as sophisticated traders and investors take advantage of them quickly.

However the put call parity relationship is important when trying to understand the relationship between different positions in an options spread.

Let’s look at an example of this:

An Illustrated Example Of Put Call Parity

We’ll just illustrate this via another example:

An investor buys 100 AAPL shares for $20,000 (ie $200/share) and then writes a 3 month AAPL 200 contract for $1500 (ie $15 per share).

(This is an example of the covered call strategy.)

At the end of the 3 months this $1500 is his/hers to keep if the price is less than $200. But note that they will have lost money on the share itself as it has fallen below his/her purchase price.

Indeed, as with all stock holders, this loss could be up to 100% in the unlikely event the share fell to zero (albeit slightly cushioned in this case by the options premium).

Above $200 the investor will have their shares ‘called away’: the options holder would exercise their option and force the investor to sell their shares at $200. Any profit due to the shares now being above $200 is forgone to the lucky options holder. But the investor does get to keep the options premium.

The profit and loss diagram for this is below. Above $200 the total profit would be the options premium. Below $200 losses are (almost) 100% of capital invested.

covered call
Covered Call

Does this remind you of anything?

Take a look at the P&L Diagram of the Bought Put Option:

Bought Put

The diagram is the covered call upside down. Thus, as we have said before the investor’s P&L Diagram is exactly the same as a sold put option.

Note the important (and hopefully self explanatory) concept that if two options position have the same P&L Diagram they are exactly the same position.

Therefore we have shown that the investor’s purchased stock and written 3 month AAPL 200 call is exactly the same as if he/she had written a 3 month AAPL 200 put. They are the same trade.

This important concept is called put call parity and crops up everywhere: it is usually the case that any call/put can be reconstructed using an alternative stock plus put/call (respectively) combination.

facebookShare on Facebook
TwitterTweet
PinterestSave

Further Reading On Options Trading...

Covered Calls Options Strategy Guide

Introduction To Covered Calls Covered calls have always been a popular options strategy. Indeed for many traders, their introduction to options trading is a covered call used to augment income ...
Read More

Options Trading Strategy: Bull Call Spread

The Bull Call Spread: A Bullish Options Strategy Introduction The bull call spread is a simple strategy that can be used by novice options traders to bet on higher prices ...
Read More

Strangle Spread: A Guide To This Options Trading Strategy

The Strangle Spread Options Trading Strategy Introduction Options, and combination trades such as the strangle spread, can be a very useful tool for both novice and seasoned traders and investors ...
Read More

Straddle Spread: Learn This Options Trading Strategy

Options Trading Strategy: Straddle Spread Introduction The straddle spread is a relatively simple options strategy that can be used under different market scenarios. However its most normal use is a ...
Read More

Options Trading Education

Options trading is a potential lucrative sideline for those willing to put in the effort. Epsilon Options is here to help you learn the skills you’ll need to become a ...
Read More

Options Spreads: Put & Call Combination Strategies

Options Combinations Explained Options spreads involve the purchase or sale of two or more options covering the same underlying stock or security (ref). These options can be puts or calls ...
Read More

Options Delta Explained: Sensitivity To Price

Options Delta is the measure of an option’s price sensitivity to the underlying stock or security’s market price. It is the expected change in options price with a 1c change ...
Read More

Options Trading Strategy: Long Call

A long call option strategy is the purchase of a call option in the expectation of the underlying stock rising. It is delta and theta positive. Introduction Options can provide ...
Read More

The Synthetic Covered Call Options Strategy Explained

What Is A Synthetic Option Strategy? A synthetic covered call is an options position equivalent to the covered call strategy (sold call options over an owned stock). It consists of ...
Read More

Options Greeks: Theta, Gamma, Delta, Vega And Rho

The options greeks - Theta, Vega, Delta, Gamma and Rho - measure option price sensitivity to changes in time, volatility, stock price and other parameters. In the world of finance, ...
Read More

Sell to Open vs Sell to Close

What is Sell to Open vs Sell to Close? We look at these two similar, but not exactly the same, concepts. There are two ways to participate in the options ...
Read More

Extrinsic Value In Options Trading

What is Extrinsic Value In Options Trading? The extrinsic value of a stock option contract is the portion of the option's worth that has been assigned to factors other than ...
Read More

Options Brokers Reviews

How To Choose The Best Options Broker There are several things an option trader needs to look for in an options broker. However, whilst most traders will need most, if ...
Read More

Options Theta Explained: Price Sensitivity To Time

Options theta measures option price sensitivity to time. Time Decay & Options Theta All things being equal options lose value over time - so called 'time decay' - and theta ...
Read More

Options Trading Strategy: Iron Condor

Introduction Options are highly versatile financial instruments. They can be used to bet on market direction, to bet on changes in implied volatility or even to collect premiums. Options can ...
Read More

Primary Sidebar

Featured Posts:

Options Spreads: Put & Call Combination Strategies

Protective Put: This Defensive Put Option Strategy Explained

Options Greeks: Theta, Gamma, Delta, Vega And Rho

How To Learn Stock Options Trading: Stock Options For ‘Dummies’

LEAP Options Explained: What Are They And How Do They Work?

Options Trading Strategy: Butterfly Spread

Copyright © 2023 · Monochrome Pro on Genesis Framework · WordPress · Log in

  • Facebook
  • Twitter
  • Pinterest
  • Privacy Policy