Put-Call Parity Calculator
The Put-Call Parity Calculator solves the relationship between a European call, a European put, the underlying spot price, and the present value of the strike price. It is not a volatility model and it does not forecast the underlying asset. Instead, it checks whether related option prices are internally consistent. Select the value to calculate, enter the other three values, and the form shows the missing call price, put price, present value of strike, or spot price.
This page is informational, not investment advice. Options and other derivatives are high-risk instruments. A parity calculation may look precise, but real trading results depend on bid-ask spreads, assignment and exercise rules, short-sale availability, dividends, margin, commissions, taxes, and execution.
Why parity matters
Put-call parity says two portfolios should have the same value today when they produce the same payoff at expiration. One portfolio combines a European call with enough discounted cash to pay the strike. The other combines a European put with the underlying asset. If both portfolios have the same expiration payoff, competitive markets should not let one cost materially more than the other after all frictions are considered.
This is the key difference between parity and the call and put option calculator. The payoff calculator shows the profit of a single long option at a target price. Put-call parity compares two linked portfolios. It also differs from the Black-Scholes option calculator, which estimates model prices from volatility, rates, dividends, and time. If you combine multiple option legs, the options spread calculator may be a better tool for expiration profit and loss.
Formula used by the calculator
The calculator uses the common parity identity:
The equivalent rearranged form is:
where C is the European call price, P is the European put price, S is the spot price of the underlying asset, and PV(K) is the present value of the strike price.
The form can also calculate present value from a strike, risk-free rate, and years to expiry. Its helper uses annual compounding:
That convention is important. Some option models use continuous compounding, while this helper uses the exact annual-compounding expression above. If you are comparing against another model, keep the rate convention consistent.
Rearranged equations
When you select a missing value, the calculation rearranges the same equation:
If the solved value is negative or not a valid number, the calculator treats the input set as invalid. Negative option prices and negative spot prices are not economically meaningful in this basic framework.
Worked example
The default setup solves for the European call price. The known values are a put price of $5, a spot price of $100, and a present value of strike of $97. The formula is call equals put plus spot minus present value of strike. Therefore the solved call is $5 plus $100 minus $97, or $8.
The calculator then checks both sides of the parity equation. The left side, call plus present value of strike, is $8 plus $97, or $105. The right side, put plus spot, is $5 plus $100, also $105. The parity difference is $0. That zero difference is the result you should expect when the missing value was solved from the other inputs.
If you instead solve for put price using call $8, spot $100, and PV strike $97, the put is $8 plus $97 minus $100, or $5. If you solve for present value of strike using call $8, put $5, and spot $100, the answer is $97. If you solve for spot using call $8, put $5, and PV strike $97, the answer is $100. Each case is the same relationship viewed from a different missing corner.
Using the present value helper
Suppose you do not know the present value of strike but you know the strike is $100, the risk-free rate is 3%, and time to expiry is 1 year. The helper calculates $100 divided by 1.03, or about $97.09. If the put is $5 and spot is $100, the parity call value using that helper is about $7.91. The small difference from the default $8 example comes from using $97.09 rather than $97 as the discounted strike.
Because the helper compounds annually, do not mix it with a continuously compounded Black-Scholes output unless you intentionally convert the rate. A small convention mismatch can look like a pricing gap when it is really just an input mismatch.
Common pitfalls
Do not compare options with different strikes or expirations. Do not use an American option pair and assume the basic European equation will hold exactly. Be careful around ex-dividend dates, hard-to-borrow shares, wide bid-ask spreads, and illiquid contracts. A theoretical arbitrage can vanish after the cost of buying one side, selling the other, posting margin, and managing exercise risk.
For practical analysis, use parity as a diagnostic. If a put looks expensive relative to a call, spot, and discounted strike, ask whether dividends, borrow, liquidity, or early exercise explain it before assuming there is a trade. The best use of this calculator is to make the relationship visible and force each input to be stated clearly.
Formula sources and scope
- Principles of Finance — OpenStax, Rice University (peer-reviewed open textbook); 2022 first edition, ISBN 978-1-951693-54-1; Jurisdiction-neutral finance definitions. Supports: European no-income parity C + PV(K) = P + S; solve algebraically for selected variable. Accessed 2026-07-09.
These sources support the stated formula or definition. Results remain estimates based on the entered values and do not replace financial, legal, tax, lending, or investment advice. Compare periods, units, accounting definitions, and jurisdiction-specific rules before acting.
Sources
- Investor.gov, Options — overview of options contracts and basic option concepts.
- Options Industry Council, Options Pricing — reference on intrinsic value, time value, and drivers of option premium.
- FINRA, Rule 4210: Margin Requirements — regulatory context for margin and option account requirements.