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 that will 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.

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, puts, and calls, are complementary with respect to both pricing and valuation. Therefore, by knowing the value of a put option you can quickly calculate the value of the complimentary call option (with the same strike price and expiration date). There are many reasons that this is important knowledge for traders and investors. It can highlight profitable opportunities that present themselves when option premiums are out of whack. Understanding put-call parity can also help you to gauge the relative value of an option you may be considering for your portfolio.

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

Option premiums have two components: intrinsic value and time 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 and 50 cents of time value. Time value represents the value of the option attributed exclusively to time. A $17 call option on silver that has a premium of 50 cents when silver is trading at $16 has no intrinsic value and 50 cents of time value. Therefore, in-the-money options have both intrinsic and time value while an out-of-the-money option has only time value. Put-call parity is an extension of these concepts.

If June gold is trading at $1200 per ounce, a June $1100 call with a premium of $140 has $100 of intrinsic value and $40 of time value. The concept of put-call parity, therefore, tells us that the value of the June $1100 put option will be $40.

As another example, if July cocoa were trading at $3000 per ton, a July $3300 put option with a premium of $325 per ton would tell us definitively that the value of the July $3300 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 as both only have time value.

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 created by combining the requisite options and futures with the same maturity and in the case of the options, the same strike prices.

Options are amazing instruments. Understanding options and put-call parity will enhance your market knowledge and open new doors of profitability and risk management for all of your investment and trading activities.

Put-call parity is an attribute of options markets that is applicable not only in commodities but in all asset markets where options markets thrive. Spend some time and understand put-call parity as it is a concept that will put you in a position to understand markets better than most other market participants giving you an edge over all competition. Success in markets is often the result of the ability to see market divergence or mispricing before others. The more you know, the better the chances of success.