If put-call parity is violated, traders could make riskless profit by combining options, the stock and borrowing. In practice it holds closely for liquid European options, after allowing for dividends and transaction costs.
How to use the Put-Call Parity Calculator
- European call option price
- Spot price of the underlying
- Strike price
- Years to expiry
- Risk-free rate (continuous)
- Every result field is editable: type into European put option price and European call option price plus every other field update to match.
Results update as you type, and every field accepts the units shown in its menu.
How it works
Enter the call price, spot price, strike price, time to expiry and risk-free rate. Type a put price into the result to solve for the call.
Tips
- Use annualised volatility and interest rates as decimals per year.
- Remember that one standard option contract usually covers 100 shares.
- Options lose time value as expiry approaches – re-run the numbers as dates change.
- Derivatives can lose more than you expect; understand the maximum loss before trading.
Common mistakes to avoid
- Mixing days and years for time to expiry.
- Ignoring commissions and the bid–ask spread.
- Forgetting dividends when pricing options on dividend-paying stocks.
Inputs explained
| Field | What to enter |
|---|---|
| European call option price | Amount in your currency |
| Spot price of the underlying | Amount in your currency |
| Strike price | Amount in your currency |
| Years to expiry | A number |
| Risk-free rate (continuous) | In % |
What each result means
- Present value of the strike price = [Strike price]×exp(-[Risk-free rate (continuous)]÷100×[Years to expiry])
- European put option price = [European call option price] + [Present value of the strike price] – [Spot price of the underlying]
- Call + PV(strike) = [European call option price] + [Present value of the strike price]
- Put + spot = [European put option price] + [Spot price of the underlying]
Example values
How the main result changes when European call option price changes and everything else stays at the example values above:
| European call option price | European put option price |
|---|---|
| 4 | 1.78 |
| 6 | 3.78 |
| 8 | 5.78 |
| 10 | 7.78 |
| 12 | 9.78 |
| 16 | 13.78 |
Formula
C + K e^(−rT) = P + SPV of strike = K × e^(−rT)Put = C + PV(K) − SWorked example
Inputs — European call option price: $8; Spot price of the underlying: $100; Strike price: $100; Years to expiry: 0.5; Risk-free rate (continuous): 4.5 %.
Results — Present value of the strike price = $97.78; European put option price = $5.78; Call + PV(strike) = $105.78; Put + spot = $105.78.
Frequently asked questions
What is put-call parity?
The relationship C + PV(K) = P + S for European options.
Does it apply to American options?
Only as an inequality, because of early exercise.
How do dividends affect it?
Subtract the present value of dividends from the spot price.
What formula does the Put-Call Parity Calculator use?
C + K e^(−rT) = P + S.