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The put/call parity is the mathematical relationship between call and put options that share the same strike price and expiration month. An example would be the QQQQ November 44 Call and the QQQQ November 44 Put. These two options are likely to have related Delta, Gammas, Theta and Vegas.

According to the put/call parity, when stock is introduced both the calls and puts have the same functionality. For example, consider two similar positions: a married put (long put and long stock the same amount of shares) and a long call. Both have identical risk graphs: limited downside and unlimited upside.

However, purchasing the married put would be much more expensive because of the capital requirement to purchase the shares of stock. Therefore, there is an opportunity cost in choosing the married put over the long call. With that being the case, why would anyone choose the married put over the long call?

Here enters the concept of arbitrage: if faced two identical choices, the investor is going to choose the least expensive one. The demand that is created for the long calls over the married put causes the call options to rise in price until there is no longer an arbitrage advantage of one over the other. Hence, the long call and married put prices move so that the call and put options (same strike and expiration) are in a state of equilibrium.

So, with that relationship satisfied we can agree that the being long a call option will have the same outcome if we were to be long stock and short a put. Hence, the married put is a synthetic form of a long call position. We can further state that both positions would yield the same profit or loss at expiration.

To create a synthetic short put position, an investor can buy stock and sell a call (again, the same amount of shares; i.e. short 1 call contract and buy 100 shares of the underlying). As shown, the common thread is that options positions have synthetic equivalents:

Long Put + Long Stock = Long Call
Short Put + Short Stock = Short Call
Long Call + Short Stock = Long Put
Short Call + Long Stock = Short Put

The main point to take away from this, other than the relationships between stocks and options, is that put/call parity is necessary for markets to be efficient. Without it, the fair value of options would not be present. Hence, the put/call parity is vital to the pricing of options.

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7.8- Put/Call Parity

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