Options: The Concept of Put-Call Parity

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Options are derivative instruments. One of the reasons that option trading and investing is so much fun is that is it like a game of chess. During the life of an option, there are so many opportunities; they can either enhance or destroy the value of a position.

There are so many moving pieces in the puzzle of options trading. The nominal option prices move higher or lower as implied volatility can move up or down, and supply and demand for options themselves will move option premiums.

Put-call parity is important in options trading. Learn more about it and how it works.

Key Takeaways

  • Put-call parity occurs when the value of a put option has an equivalent call option.
  • The options will have the same strike price and expiration date.
  • Understanding put-call mispricing gives you a better chance of market success.

What Is Put-Call Parity?

Put-call parity is a concept that anyone involved in options markets needs to understand. Parity is a functional equivalence. The genius of option theory and structure is that two instruments are complementary with respect to both pricing and valuation: puts and calls.

By knowing the value of a put option, you can quickly find the value of the complimentary call option with the same strike price and expiration date. There are many reasons that this is important. It can highlight profitable opportunities that present themselves when option premiums are off. Understanding put-call parity can also help you to gauge the relative value of an option.

There are two styles of options: American and European. The exercise of American options can be at any time during their life. The exercise of European options only occurs on the options' expiration date. In most cases, put-call parity only works perfectly with European style options.

What Are Examples of Put-Call Parity?

Option premiums have two components: intrinsic value and time value (or extrinsic value). Intrinsic value is the in-the-money portion of the option. A $15 call option on silver with a premium of $1.50 when silver is trading at $16 has $1 of intrinsic value; it therefore also has 50 cents of time value.


Time value represents the value of the option attributed exclusively to time.

What about a $17 call option on silver that has a premium of 50 cents when silver is trading at $16? It would contain no intrinsic value and only 50 cents of time value. Therefore, in-the-money options have both intrinsic and time value; an out-of-the-money option has just time value. Put-call parity is an extension of these concepts.

If gold is trading at $1,200 per ounce in June, a $1,100 call with a premium of $140 has $100 of intrinsic value and $40 of time value. The concept of put-call parity tells us that the value of the June $1,100 put option will be $40.

Here's another example: If in July cocoa were trading at $3,000 per ton, a July $3,300 put option with a premium of $325 per ton would tell us definitively that the value of the July $3,300 call option is $25 per ton. As you might imagine, call and put options that are at-the-money (strike prices equal to the current futures price) with the same expiration and strike price (straddles) will trade at the same price; both only have time value.

What Are the Formulas?

To bring this all together, there are some simple formulas to remember for European style options:

  • Long Call + Short Future = Long Put (same strike price and expiration)
  • Long Put + Long Future = Long Call (same strike price and expiration)
  • Long Call + Short Put = Long Future (same strike price and expiration)
  • Long Put + Short Call = Short Future (same strike price and expiration)

These types of positions are synthetic positions. They are created by combining the requisite options and futures with the same maturity and in the case of the options, the same strike prices.

The Bottom Line

Options are amazing instruments. Understanding options and put-call parity will enhance your market knowledge. It can open new doors of profitability and risk management.

Put-call parity is an attribute of options markets. It is applicable not only in commodities but in all asset markets where options markets thrive. Spend some time, and learn to understand put-call parity. It is a concept that will put you in a position to understand markets better than most other market participants, which can give you an edge over the competition.

Success in markets is often the result of the ability to see market divergence or mispricing before others do. The more you know, the better your chances of success.