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 and the market is fairly priced. If they differ, arbitrage may be possible:
- Left side (C - P) > Right side (S - PV(K)): the call is expensive relative to the put. Sell the call, buy the put, buy the stock, borrow PV(K). This is a conversion.
- Left side < Right side: the put is expensive. Buy the call, sell the put, short the stock, lend PV(K). This is a reversal.
Either way the position is fully hedged: long stock plus a long put plus a short call at the same strike is worth exactly K at expiry no matter where the stock goes, so the loan repays itself and you keep the difference you collected at the start. That is what makes it arbitrage rather than a bet.
Dividends
A dividend paid before expiry belongs to the stockholder, not to the call holder, so it pulls the stock leg down and the parity relationship becomes:
C - P = S - PV(K) - PV(Dividends)
Leave the dividend field at zero for an index or a non-payer. Enter the total cash expected per share otherwise. The calculator discounts it from the midpoint of the period, which is close enough unless the ex-date sits right at one end.
Skipping this is the most common way people convince themselves they have found free money on a dividend-paying stock. On a 3% yielder over six months you are looking for a mispricing of a few cents while ignoring about 1.5% of the share price.
Important limitations:
- Applies only to European options, not American ones, which can be exercised early
- Real markets have transaction costs, bid-ask spreads, and short-selling constraints that often prevent pure arbitrage
- The borrow rate on a hard-to-borrow stock can swamp the entire discrepancy
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.
SuperGlobalCalculator is independently built and maintained. See how we build and verify our calculators.