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.