A European call and put with the same strike and expiry are tied to the underlying’s spot price by a no-arbitrage relationship — given any three of the four key values, the fourth is fully determined.
How it works
Discounting the strike price back to today at the risk-free rate, then subtracting spot price from call price and adding that discounted strike, gives the put price parity requires.
What this does not include
This does not include dividends on the underlying (which shift the parity relationship), American-style early-exercise features, or transaction costs — all of which can cause a real market quote to deviate from the pure parity relationship shown here.
How to use this calculator
- Enter spot price, strike price, risk-free rate, time to expiry, and the call price.
Frequently asked questions
What does it mean if a real put price differs from this result?
In a liquid, efficient market it usually signals the relationship is temporarily out of line (or that dividends, borrowing costs, or American-exercise value explain the gap) — traders sometimes exploit such mismatches through arbitrage.
Does put-call parity apply to American options?
Not exactly — American options carry early-exercise value that breaks the strict equality, though a similar inequality-based relationship still holds.
Why use discrete compounding here instead of continuous?
Discrete annual compounding is simpler to follow for most users and gives a very close approximation to the continuously-compounded textbook version for typical rates and time horizons.
