Put-Call Parity Calculator
Parity Calculation Result
What Is the Put-Call Parity Calculator?
A put-call parity calculator is a tool that estimates one missing value in the relationship between a European call option, a European put option, the underlying spot price, the strike price, the risk-free rate, and time to expiration.
This calculator solves for the theoretical call option price, theoretical put option price, implied spot price, or implied strike price. It helps users compare the relationship between paired call and put options with the same expiration and strike. The result is an estimate based on continuous compounding and the calculator’s stated assumptions.
The put-call parity calculator answers a simple question: given the other required inputs, what value keeps the option relationship in parity? It is useful for learning options pricing, checking whether inputs are internally consistent, and spotting cases where the calculator shows a negative theoretical result.
How the Put-Call Parity Formula Works
The calculator uses the continuous compounding form of put-call parity. It treats the strike price as a future value and discounts it back to present value using the risk-free interest rate and time to expiration.
In these formulas, C is the call option price, P is the put option price, S is the spot price of the underlying asset, K is the strike price, r is the annual risk-free interest rate written as a decimal, and T is time to expiration in years. The calculator sets T as days to expiration divided by 365.
For example, choose “Call Option Price (C)” as the variable to solve for. Enter a put price of $3.25, a spot price of $100, a strike price of $95, a risk-free interest rate of 4.5%, and 30 days to expiration. The time value is 30 ÷ 365, or about 0.0822 years.
The present value of the strike is 95 × e-(0.045 × 0.0822), which is about $94.6493. The call price is then 3.25 + 100 - 94.6493 = 8.6007. The calculator displays this as about $8.6007, formatted with a dollar sign and two to four decimal places.
If the calculated value is below zero, the result area displays “Arbitrage Implied” instead of a dollar amount. This means the entered values produce a negative theoretical price under the calculator’s parity equation.
How to Use the Put-Call Parity Calculator: Step by Step
- Select the variable you want to solve for under “Variable to Solve For.” You can choose call option price, put option price, spot price, or strike price.
- Enter the visible option prices and market values required for that mode. The calculator hides the field for the value it will calculate.
- Enter the risk-free interest rate as a percentage. For example, enter 4.5 for 4.5%, not 0.045.
- Enter the number of days to expiration. The calculator converts this into years by dividing the number of days by 365.
- Click “Calculate” to show the parity calculation result.
- Use “Reset” to clear all fields and return the calculator to its default call price mode.
The output shows the specific value calculated for your selected mode. Depending on your selection, the label may read “Theoretical Call Price (C),” “Theoretical Put Price (P),” “Implied Spot Price (S),” or “Implied Strike Price (K).” A normal positive result appears as a dollar value. A negative result appears as “Arbitrage Implied.”
What Your Put-Call Parity Result Means
The result is a theoretical parity value based on the inputs you provide. It does not predict where an option will trade. Instead, it checks what one value would need to be for the put-call parity equation to balance under the calculator’s assumptions.
Input and Output Summary
| Field | How the Calculator Uses It |
|---|---|
| Variable to Solve For | Controls whether the calculator returns C, P, S, or K. |
| Call Price ($) | Used when solving for put price, spot price, or strike price. |
| Put Price ($) | Used when solving for call price, spot price, or strike price. |
| Spot Price ($) | Used when solving for call price, put price, or strike price. |
| Strike Price ($) | Used when solving for call price, put price, or spot price. |
| Risk-Free Interest Rate (%) | Converted to a decimal and used for continuous compounding. |
| Days to Expiration | Divided by 365 to calculate time in years. |
Assumptions Behind the Calculation
The calculator states that it assumes non-dividend-paying European options and continuous compounding for the present value of the strike price. That matters because American options, dividend-paying stocks, transaction costs, bid-ask spreads, borrowing constraints, and real market frictions can change how parity works in practice.
Limitations to Keep in Mind
This is an estimate, not financial advice. Real option prices may differ because of market conditions, volatility expectations, liquidity, interest rate changes, dividends, early exercise rights, fees, taxes, and brokerage rules. The calculator also does not include volatility, option Greeks, implied volatility, probability of profit, or an options payoff chart.
The calculator requires the visible fields for the selected mode. If a required field is blank, it does not display a result. Numeric inputs are set with a minimum value of zero, and days to expiration uses whole-number steps in the input field.
Frequently Asked Questions
What is put-call parity?
Put-call parity is a pricing relationship between a European call option, a European put option, the underlying spot price, the strike price, interest rate, and time to expiration. This calculator uses that relationship to solve for one missing value when the other required inputs are entered.
How do I calculate a call price with put-call parity?
To calculate a call price, select “Call Option Price (C)” and enter the put price, spot price, strike price, risk-free interest rate, and days to expiration. The calculator discounts the strike price using continuous compounding, then calculates C = P + S - K e-rT.
How do I calculate a put price with put-call parity?
To calculate a put price, select “Put Option Price (P)” and enter the call price, spot price, strike price, risk-free interest rate, and days to expiration. The calculator finds the present value of the strike, adds it to the call price, and subtracts the spot price.
Why does the calculator say Arbitrage Implied?
The calculator says “Arbitrage Implied” when the computed target value is negative. Under the calculator’s parity equation, a negative theoretical price means the entered inputs do not create a normal positive result. The tool describes this as a possible mispricing or arbitrage opportunity.
Is this put-call parity calculator for American options?
No, the calculator states that it assumes European options. European options are modeled without early exercise in this parity relationship. American options can behave differently because they may allow early exercise, so the calculator’s result should not be treated as an American options pricing model.
Does the calculator include dividends?
No, the calculator states that it assumes non-dividend-paying options. It does not include dividend yield, scheduled dividends, or dividend adjustments in the formula. If the underlying asset pays dividends, real option pricing may differ from the result shown by this calculator.
How accurate is the put-call parity calculator?
The calculator is accurate to its coded formula and assumptions when the inputs are valid. It uses continuous compounding, a 365-day year, and the values you enter. Real market prices can still differ because of bid-ask spreads, liquidity, dividends, exercise style, fees, and changing interest rates.