Put-Call Parity is a fundamental options pricing principle that establishes a mathematical relationship between the price of a European put and call option on the same underlying with the same strike price and expiration date. The formula is: C − P = S − PV(K), where C is call price, P is put price, S is current stock price, and PV(K) is the present value of the strike price.
In practice, this means that if you know the call price, the stock price, the strike, and the risk-free rate, you can calculate exactly what the put should be worth — and vice versa. Arbitrageurs ensure this relationship holds in liquid markets.
For Wheel Traders: Understanding put-call parity helps explain why IV is the same for equivalent puts and calls (same strike, same expiration) — a concept called "volatility skew" when they differ. It also underpins the logic of synthetic positions.
Examples of Put-Call Parity in Action
- 1If a $100 call trades at $3.00, the stock is at $100, and the risk-free rate is 5% with 30 days to expiration, the $100 put must trade at approximately $2.63 to prevent arbitrage.
- 2A put and call on SPY with the same strike and expiration reflecting the same implied volatility — this is put-call parity in practice.