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Put–Call Parity Calculator — result sheet
Check the no-arbitrage relationship between European call and put premiums, the underlying price, strike, rates, dividends, and time to expiry.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: C−P = S·e^(−qT) − K·e^(−rT); parity-implied P = C − S·e^(−qT) + K·e^(−rT), parity-implied C = P + S·e^(−qT) − K·e^(−rT), and residual = C−P−[S·e^(−qT)−K·e^(−rT)].
Put–call parity is a relationship between otherwise matching European options. The calculator discounts the underlying’s continuous dividend yield and the strike’s continuously compounded risk-free rate, then reports the parity-implied premium in either direction and the residual from the two entered premiums. It is a consistency check for a stated model, not a live arbitrage signal or a trading recommendation.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Underlying price S — currency; minimum 1.0E-6; maximum 1000000000
- Strike price K — currency; minimum 1.0E-6; maximum 1000000000
- Time to expiry T — years; minimum 1.0E-6; maximum 100
- Continuously compounded risk-free rate — %; minimum -100; maximum 1000
- Continuous dividend yield — %; minimum -100; maximum 1000
- European call premium C — currency; minimum 0; maximum 1000000000
- European put premium P — currency; minimum 0; maximum 1000000000
Worked example
| Input | Value |
|---|---|
| Underlying price S | 100 |
| Strike price K | 100 |
| Time to expiry T | 1 |
| Continuously compounded risk-free rate | 5 |
| Continuous dividend yield | 0 |
| European call premium C | 10.45 |
| European put premium P | 5.57 |
The parity difference is about 4.8771; the call-implied put is about 5.5729 and the entered pair has a small residual from rounding.
Assumptions and limits
- The call and put are European, have the same underlying, strike, expiry, currency, and settlement convention.
- Rates and dividend yield are continuously compounded annual rates and are constant over the entered time.
- The underlying can be held or financed under the idealized no-arbitrage relationship, with no transaction costs, bid–ask spread, margin friction, taxes, or trading restrictions.
- The residual is an arithmetic model difference; a nonzero value does not by itself prove an executable arbitrage opportunity.
- The calculator does not estimate volatility, option Greeks, early exercise value, discrete dividends, or market liquidity.
- Use the page for education and model reconciliation, not personalized investment advice.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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