Put-Call Parity Essentials
Before the creation of the Black-Scholes model, option pricing was hardly
an exact science. Traders had only a few mathematical tools available to
compare the relative prices of options. One such tool, put-call parity, stems
from the fact that puts and calls on the same class sharing the same month
and strike can have the same functionality when stock is introduced.
For example, traders wanting to own a stock with limited risk can buy a
married put: long stock and a long put on a share-for-share basis. The
traders have infinite profit potential, and the risk of the position is limited
below the strike price of the option. Conceptually, long calls have the same
risk/reward profile—unlimited profit potential and limited risk below the
strike. Exhibit 6.1 is an overview of the at-expiration diagrams of a married
put and a long call.
EXHIBIT 6.1 Long call vs. long stock + long put (married put).
Married puts and long calls sharing the same month and strike on the
same security have at-expiration diagrams with the same shape. They have
the same volatility value and should trade around the same implied
volatility (IV). Strategically, these two positions provide the same service to
a trader, but depending on margin requirements, the married put may
require more capital to establish, because the trader must buy not just the
option but also the stock.