Currency Option Put-Call Parity Calculator
Compare entered European currency call-minus-put premiums with discounted spot-minus-strike put-call parity for the same pair, strike and expiry. The result is a mathematical consistency diagnostic, not an executable arbitrage claim.
Enter one matched call-and-put case
The call and put must share the same European underlying orientation, strike, expiry, settlement assumptions and observation time. Enter both premiums as quote currency per one base unit.
Discounted put-call parity diagnostic
Derived from FX Option Scenario, Parity and Greeks model 1.0.0.
How currency-option put-call parity is checked
European put-call parity links a call and put with the same underlying orientation, strike and expiry to discounted spot and strike cash flows. In the page convention, spot is quote currency per one base currency. The quote-currency rate discounts the strike payment, while the base-currency rate discounts the underlying base-currency leg.
The calculator subtracts the entered put premium from the entered call premium and compares that amount with discounted spot minus discounted strike. A result near zero means the manually entered values satisfy the disclosed identity within numerical and input precision. A positive or negative residual only shows the direction of that arithmetic difference.
The two forward diagnostics rearrange the same relationship. Rate-parity forward uses spot and the two entered continuous rates. Premium-implied forward uses strike and entered call-minus-put premium after undoing quote-currency discounting. Matching values are another representation of a near-zero residual, not independent market evidence.
Both premiums must use the same unit and timestamp. Combining a call ask with a put bid, quotes observed at different times, different exercise styles, different expiry cuts, different settlement terms or different premium currencies violates the matched-contract assumption even if each input is individually real.
A displayed residual is not an executable arbitrage opportunity. A real conversion or reversal requires synchronized tradable prices, financing, ability to transact in the underlying or forward, collateral, exercise and settlement mechanics, taxes, credit capacity and enough size after costs. This page observes none of those conditions.
The direct base notional multiplies the per-unit residual only to make scale visible. It does not infer a standard lot, exchange contract multiplier or executable quantity. Actual OTC, exchange and broker products can use different deliverables, ticks, premiums and settlement conventions.
Worked example from the audited fixture
The audited fixture uses EUR/USD spot 1.10000, strike 1.12000, 4% USD quote-currency continuous rate, 2% EUR base-currency continuous rate, 180 days on a 365-day basis and EUR 100,000 reference notional.
Entered call premium is USD 0.0324689310779 per EUR and entered put premium is USD 0.0413882467444 per EUR. Call minus put is −0.0089193156665, while discounted spot minus strike is the same within floating-point precision.
The displayed residual rounds to zero. Both the rate-parity forward and premium-implied forward are 1.11090299. Those values reproduce one consistent model fixture; they are not a live forward or arbitrage test.
How to interpret the result
- Confirm the call and put are truly matched before reading the residual. Same currency symbols alone are not enough.
- Treat a tiny residual as numerical consistency with the disclosed identity, not proof that either premium is fair or executable.
- Treat a material residual as a prompt to recheck units, timestamp, rate orientation, exercise style, strike, expiry cut and settlement before considering any market explanation.
- Use the total residual only as the per-unit difference multiplied by entered notional. It is not attainable profit and contains no transaction or financing costs.
- Compare both forward diagnostics as a secondary arithmetic check; neither value is a dealer quote, deliverable forward price or accounting fair value.
- Use the pricing calculator when volatility is known and a theoretical premium is needed; parity itself does not require volatility.
Which FX option analysis tool answers which question?
These tools share governed European FX-option arithmetic but keep three different user jobs separate. A scenario changes one option state, parity checks matched premiums, and portfolio Greeks aggregate local multi-leg exposures.
| Tool | Required entered data | Output | Hard boundary |
|---|---|---|---|
| Price scenario | One option, entered premium and two model states | Before-expiry model P&L scenario | No forecast or executable close |
| Put-call parity | Matched call/put premiums, spot, strike, rates and time | Discounted consistency residual | No executable-arbitrage verdict |
| Portfolio Greeks | Shared pair state plus one to twenty option legs | Signed premium, delta, gamma and vega | No account retrieval or hedge instruction |
Assumptions and limitations
- No option chain, bid, ask, spot feed, forward feed, yield curve, account, contract, position, order, exercise or settlement system is connected.
- European same-contract parity is assumed. American exercise, barriers, digitals, differing collateral and settlement mismatches are excluded.
- Rates are entered as constant continuously compounded annual rates for the entered horizon; term structures and funding asymmetry are omitted.
- Bid-ask spread, commissions, tax, funding, collateral, credit, liquidity, borrow, conversion and operational costs are not calculated.
- A residual can reflect inconsistent or stale manual inputs. The tool cannot distinguish data error from a market or convention difference.
- No arbitrage, fair value, premium, forward, option, provider, broker, hedge, strategy, signal or trade is recommended or certified.
Sources and methodology
The arithmetic is independently fixture-tested. These primary references define formulas and sensitivity meanings; they do not verify an entered premium, quote, contract, provider, position or market timestamp.
- LCH — Options Valuation Formulas — Primary clearing methodology for discounted FX-option pricing and parity components.
- Garman and Kohlhagen — Foreign Currency Option Values — Original two-interest-rate European currency-option model reference.
- CME Group — Understanding Put-Call Parity — Primary-market education reference for same-strike, same-expiry European parity relationships.
Frequently asked questions
- It compares entered call minus put premium with discounted spot minus discounted strike for matched European options.
- Yes. They must also share the same underlying orientation, expiry, exercise style, settlement assumptions and observation time.
- No. The identity uses matched premiums, spot, strike, two discount rates and time; volatility is not an input.
- It means the entered values satisfy the disclosed discounted identity within numerical and input precision.
- No. Executable arbitrage depends on synchronized tradable prices, spreads, funding, collateral, taxes, credit and settlement that this page does not observe.
- They are equivalent rearrangements of parity: one from spot and rates, the other from strike and the entered premium difference.
- That creates a particular executable-side comparison only if every other leg and cost is synchronized and tradable; this calculator does not verify that setup.
- No. It is only the per-unit arithmetic residual multiplied by the entered base notional.
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