Advanced tool for call, put, and forward parity. Inspect discounting, valuation gaps, and implied relationships. Built for clear decisions across pricing scenarios and studies.
Use three known option-parity values, plus rate and time, to solve the remaining field.
The line shows theoretical C - P across strike values using the entered forward price and discount factor.
Main forward-based parity:
C - P = DF × (F - K)
Where C is call price, P is put price, F is forward price, K is strike, and DF is the discount factor.
Discount factor options
DF = e^(-rT) for continuous compounding
DF = (1 + r/m)^(-mT) for discrete compounding
Useful rearrangements
C = P + DF × (F - K)
P = C - DF × (F - K)
F = K + (C - P) / DF
K = F - (C - P) / DF
This version is practical for financial engineering checks because it works directly from forward inputs instead of requiring a separate spot-dividend adjustment.
Put call parity is a no-arbitrage pricing relationship linking calls, puts, forwards, discounting, and strike value. If market prices break that relationship by more than costs and frictions, a pricing inconsistency exists. Traders, analysts, and financial engineers use it to validate models and detect mispricing.
| Case | Call | Put | Forward | Strike | Rate % | Years | Compounding | Parity Gap |
|---|---|---|---|---|---|---|---|---|
| Solve Call | 13.179167 | 7.400000 | 108.000000 | 102.000000 | 5.00 | 0.75 | Continuous | 0.000000 |
| Solve Put | 6.300000 | 10.220795 | 96.000000 | 100.000000 | 4.00 | 0.50 | Continuous | 0.000000 |
| Solve Forward | 11.100000 | 8.250000 | 108.062768 | 105.000000 | 6.00 | 1.20 | Continuous | 0.000000 |
It is a no-arbitrage relationship connecting call price, put price, strike, forward value, discounting, and maturity. If quoted prices violate the relationship, the market may contain a pricing inconsistency after allowing for costs, spreads, and execution limits.
Forward-based parity is convenient when you already know or model the forward directly. It avoids separate carry adjustments in the main equation and fits many financial engineering workflows, derivatives checks, and desk-level validation tasks.
The parity gap is the difference between the observed call-minus-put spread and the theoretical discounted forward-minus-strike spread. A value near zero suggests consistency. A larger gap signals possible mispricing, bad assumptions, or missing market frictions.
A synthetic forward is the forward value implied by call and put prices under parity. It helps compare option quotes against the actual forward market and is useful when checking model outputs, broker sheets, or implied trading relationships.
Use the convention that matches your model or quoted market inputs. Continuous compounding is common in theory and some valuation models. Discrete compounding can better match annual, semiannual, quarterly, or monthly rate conventions.
It is equivalent in spirit, but the input form differs. Spot-based parity uses spot price and carry terms. This version starts from forward price, which already embeds carrying effects under the chosen assumptions.
Quoted prices can appear to fail because of bid-ask spreads, dividends, borrowing costs, taxes, collateral rules, execution delays, or stale data. Small differences do not always imply a clean arbitrage trade.
It is useful for students, quants, analysts, and financial engineers who need a fast parity check. It also helps in classroom demonstrations, valuation audits, sensitivity reviews, and model debugging.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.