Put-Call Parity Calculator
Verify put-call parity for European options.
Enter call price, put price, strike, spot, risk-free rate, and expiry to check for arbitrage opportunities.
Put-Call Parity
Put-call parity is a fundamental relationship that must hold between European call and put prices on the same underlying asset, strike price, and expiration date. If it breaks, a risk-free arbitrage profit is theoretically possible.
The formula:
C + PV(K) = P + S
Rearranged:
C - P = S - PV(K)
Where PV(K) = K × e^(-r × T)
| Variable | Meaning |
|---|---|
| C | Call option price |
| P | Put option price |
| S | Current spot (stock) price |
| K | Strike price |
| r | Continuously compounded risk-free rate |
| T | Time to expiration (in years) |
| PV(K) | Present value of the strike price |
How to read the result:
If the two sides of the equation are equal, parity holds — the market is fairly priced. If they differ, arbitrage may be possible:
- Left side (C - P) > Right side (S - PV(K)): Call is overpriced relative to put: sell call, buy put, buy stock, borrow PV(K)
- Left side < Right side: Put is overpriced: buy call, sell put, short stock, lend PV(K)
Important limitations:
- Applies only to European options (not American options, which can be exercised early)
- Real markets have transaction costs, bid-ask spreads, and short-selling constraints that often prevent pure arbitrage
- Dividends affect parity: the formula above assumes no dividends
- With dividends: C - P = S - PV(K) - PV(Dividends)
Why it matters: Put-call parity is used to synthetically create options positions, price options relatively, and detect mispricings across related contracts.
How we build and check this calculator
This calculator runs entirely in your browser, so the numbers you enter stay on your device. The math behind it is written by hand and tested against worked examples and standard references before the page goes live.
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