Put-call parity is an important concept in options trading that shows the relationship between the price of a call option, a put option, and the stock price. It helps traders understand if the options are fairly priced and allows them to find arbitrage opportunities. This principle is useful for building strategies and avoiding price mismatches in the options market.

What Is Put-Call Parity in Options Trading?

Put-call parity is a rule in options trading that shows a link between call options, put options, and the stock price. It explains how the price of a call option, minus the price of a put option, should equal the stock price minus the present value of the strike price. This relationship helps ensure fair pricing between options and the underlying asset.

Why Is Put-Call Parity Important for Traders?

Put-call parity is important because it helps traders check if options are priced correctly. If the relationship does not hold, it may create an arbitrage opportunity—where a trader can make risk-free profit by buying undervalued options and selling overvalued ones. This keeps the market balanced and prevents major pricing errors in options trading.

What Is the Put-Call Parity Formula?

The formula for put-call parity is:

       C - P = S - K / (1 + r)^t     

Where:
C = Price of call option
P = Price of put option
S = Current stock price
K = Strike price
r = Risk-free interest rate
t = Time to expiry

This formula helps confirm if the options are correctly valued with respect to the stock and interest rates.

How Does Put-Call Parity Prevent Arbitrage?

When the put-call parity balance is broken, traders can take advantage of the mispricing to make risk-free profit. For example, if the call is too expensive compared to the put and stock price, traders can sell the call, buy the put, and stock to earn a guaranteed return. This trading action brings the prices back to balance, preventing long-term arbitrage chances.

Can Put-Call Parity Help in Strategy Building?

Yes, put-call parity helps traders build strong options strategies. By understanding the link between calls, puts, and stock prices, traders can plan synthetic positions like synthetic long or synthetic short. These strategies mimic real positions using options and can be used to reduce costs or manage risk better in the market.

When Does Put-Call Parity Not Work?

Put-call parity may not work well in real markets if there are transaction costs, taxes, or liquidity issues. If the interest rate is not stable or the options are not European-style (exercisable only at expiry), then the relationship may not hold exactly. Still, it gives a strong base to understand how calls and puts should be priced fairly.