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.
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 + S
PV of strike = K × e^(−rT)
Put = C + PV(K) − S
Worked 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.