This principle defines the relationship between the price of European Call options and European Put options of the same class (i.e., same underlying asset, same strike price and same expiration date).
In simple terms, it shows that the value of a European call with a certain exercise price and exercise date can be deducted from the value of a European put with the same exercise price and exercise date.
Or, we can say that if we hold Long position in European Call and short position in European Put at the same time for the same asset class, we will get the same return as holding one forward contract on the same underlying asset with the same expiration and one forward contract on the same underlying asset with the same expiration and a forward price equal to option’s strike price.
Understanding Put Call Parity with Example
The equation for expressing put-call parity is:
C + PV(X) = P + S
C = price of the European call option
PV(X) = the present value of the strike price (x), discounted from the value on the expiration date at the risk-free rate
P = price of the European put
S = spot price, the current market value of the underlying asset
Note: this relationship holds true for European options and not for American Options. For American options we need to modify the equation after adjusting for dividends and interest rates.
If this relationship does not hold true then an arbitrage opportunity will exist. Such opportunities are uncommon and short lived in liquid markets.
C – P = S – PV(X)
If Reliance is trading at Rs.1500 and you checked option prices for Reliance with the strike price 1460, you might see Call Option price at Rs. 100 and Put Option price at Rs. 40 (100 – 40 = 1500 – 1460).
If the call was trading higher, you could sell the call, buy the put, buy the stock and lock in a risk-free profit. It should be noted, however, that these arbitrage opportunities are extremely rare and it’s very difficult for individual investors to capitalize on them, even when they do exist. One of the reasons is that individual investors would simply be too slow to respond to such a short-lived opportunity. But the main reason is that the market participants generally prevent these opportunities from existing in the first place.
Synthetic Relationships: The combination on the right hand side will give the same return as given by the left hand side positions.
An Example of payoffs from two different synthetics portfolios:
Portfolio A = Call + Cash, where Cash = Call Strike Price
Portfolio B = Put + Underlying Asset
It can be observed from the diagrams below that the expiration values of the two portfolios are the same.
Call + Cash = Put + Underlying Asset