Put Call Parity Calculator

Verify European put-call parity or solve one missing call, put, spot, or strike input from quoted prices, rates, dividends, and time to expiry.

European put-call parity check Verify whether quoted call and put prices line up with parity, or solve one missing market input from spot, strike, rates, dividends, and time to expiry.

Mode

Display currency

Switch the money display without changing the parity assumptions.

Result

$0.20

Parity gap with 0.25 years to expiry, 4.5% rates, and 1% dividend yield.

Call price
$7.20
Put price
$4.15
Prepaid spot value
$101.75
Present value of strike
$98.90
Call side screens rich to parity The remaining parity gap is $0.20. Treat this as a pricing consistency check rather than a guaranteed arbitrage signal, because dividends, borrow costs, fees, and exercise features can shift real trading outcomes.

Spot price

$102.00

Underlying cash market input.

Strike price

$100.00

Future exercise price.

Parity gap

$0.20

Call minus put versus discounted carry relationship.

Planning note

This calculator applies European-style put-call parity with continuous compounding: C - P = S e^(-qT) - K e^(-rT). It is a consistency check, not a live executable trade recommendation.

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Parity Check

Put-call parity calculator guide: parity gap, synthetic equivalence, and one-variable solve

A put-call parity calculator checks whether quoted option prices line up with the theoretical relationship between calls, puts, the underlying, discounted strike value, and any carry adjustment for dividends. That relationship matters because it is one of the cleanest ways to test whether a European-style option price is internally consistent with the rest of the market inputs rather than just viewed on its own.

What put-call parity is measuring

Put-call parity links a call and a put with the same strike and the same expiry to the underlying asset and the present value of the strike price. In its simplest form, the relationship shows that a call minus a put should equal the prepaid cost of holding the underlying minus the discounted strike. If quoted prices deviate from that relationship, the difference is commonly described as the parity gap.

This calculator can either verify the gap directly or solve for one missing variable when the others are known. That makes it useful for checking whether a call premium looks too rich or too cheap relative to the paired put, or for inferring a parity-consistent spot, strike, call, or put value from the rest of the entered assumptions.

Why discounted strike and dividend carry matter

Put-call parity is not just call price minus put price. The strike price is a future cash amount, so it needs to be discounted back to the present using the risk-free rate and time to expiry. If the underlying pays dividends or has a carry adjustment, the spot side must also be adjusted. That is why the same stock and strike can have a different parity relationship when rates or dividend assumptions change.

Those discounting steps are also why parity is a cleaner fit for European-style valuation than for real-world execution. The identity is extremely useful for checking consistency, but actual market prices can still reflect trading frictions, borrow cost, liquidity, and exercise-style differences that push the observed quotes away from the textbook relationship.

C - P = S × e^(-qT) - K × e^(-rT)

European-style put-call parity with continuous dividend yield and continuous discounting.

Parity gap = Call price - Put price - [Prepaid spot - Present value of strike]

Shows how far the entered prices sit above or below the parity-consistent relationship.

Call price = Put price + Prepaid spot - Present value of strike

Rearranges the parity identity to solve one missing variable when the others are known.

What a positive or negative parity gap does and does not mean

A positive parity gap means the call side appears rich relative to the put and carry assumptions entered. A negative gap means the put side appears rich instead. That is a consistency signal, not a free-money guarantee. Real trading can involve bid-ask spreads, financing frictions, stock-borrow constraints, dividend uncertainty, fees, and exercise features that all affect whether an apparent mispricing can actually be used in practice.

That is why this calculator frames parity as a diagnostic rather than as a trading instruction. The result is strongest when the options truly share the same strike and expiry and when the dividend and rate assumptions are realistic. The further you move from those conditions, the more the parity gap becomes an educational guide rather than an executable conclusion.

What this parity tool does not cover

This calculator does not estimate implied volatility, Greeks, early exercise value, bid-ask spread impact, stock-borrow cost, or hard-to-borrow constraints. It also does not attempt to build or cost a real synthetic position. It is a parity identity checker only.

Use it as a market-consistency tool for European-style framing. If you need theoretical option valuation from volatility and time instead of just a carry relationship, use the Black-Scholes calculator alongside this parity page.

Further reading

Frequently asked questions

Why can parity still show a gap even when the inputs look reasonable?

Because real options markets include bid-ask spreads, borrow costs, dividend uncertainty, fees, and exercise-style differences that can push quotes away from the textbook identity even when the underlying logic is sound.

 Does put-call parity work the same way for American-style options?

Not exactly. The clean equality is strongest for European-style options. Early exercise flexibility can make American-style options deviate from the simpler parity relationship.

 Why does this calculator ask for dividend yield?

Because dividends reduce the prepaid spot value over the life of the option. Ignoring that carry effect can create a misleading parity check for dividend-paying underlyings.

 Can I use this calculator to solve a missing call or put price?

Yes. The parity identity can be rearranged to solve one missing option or cash-market input, as long as the other required variables are entered consistently.

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