Put-call parity

Put-call parity is a pricing relationship that links the price of a call option, the price of a put option, the strike price, and the price of the underlying stock, when both options share the same strike price and expiration date. It shows that a call and a put on the same terms are not independent prices set separately by the market, they are mathematically tied together through the cost of holding the underlying stock and the time value of money.

The relationship exists because a call option combined with cash equal to the present value of the strike price produces the same payoff at expiration as owning the stock plus a protective put on it. If the two sides of that equation ever priced too far apart, a trader could construct a nearly risk free trade by buying the cheaper combination and selling the more expensive one, capturing the difference. That arbitrage opportunity is exactly what keeps put and call prices in line with each other in liquid, efficiently traded options markets.

The formula is:

Put-call parity matters to options traders because it shows how a call, a put, and a position in the underlying stock are all connected, and it is the foundation for constructing synthetic positions, such as replicating a long stock position using only options. When the relationship breaks down in the real world, even briefly, it usually signals a mispricing that professional traders will move quickly to arbitrage away.