FX Option Portfolio Greeks Calculator
Aggregate signed Garman-Kohlhagen model premium, unadjusted spot delta, gamma and one-volatility-point vega across one to twenty manually entered European currency-option legs on the same base/quote pair. No account or option chain is connected.
Enter shared pair assumptions and option legs
All legs use the same spot, currency orientation, continuous rates and year basis. Each leg can have its own call/put type, long/short side, strike, flat volatility, remaining days and direct base notional.
Entered portfolio model sensitivities
Derived from FX Option Scenario, Parity and Greeks model 1.0.0.
How multi-leg FX option Greeks are aggregated
Each leg is independently priced through the governed Garman-Kohlhagen European currency-option engine. Long legs receive a positive sign and short legs a negative sign. The page then adds signed premium and local sensitivities without assuming that strikes, volatilities or expiries are identical.
All legs share one spot rate and one base/quote orientation. The quote-currency continuous rate is domestic in the formula and the base-currency continuous rate behaves like a foreign yield. Mixing EUR/USD and USD/JPY legs, reversed quotations or account-currency conversions in one run would make the displayed units incoherent, so those jobs require separate calculations.
Net spot delta is expressed in base-currency units under the unadjusted spot-delta convention. A result of +10,000 means the local model value changes like a long 10,000 base-unit spot exposure for an infinitesimal move, before higher-order effects. It is not a broker hedge order or a guarantee of the realized price change.
Net gamma is the modeled change in base-unit delta for a one-full-unit spot-rate move. Because a full move can be enormous for an exchange rate, gamma should usually be used through a small-move approximation and full repricing should be used for meaningful shocks. Long plain-vanilla legs contribute positive gamma; short legs contribute negative gamma.
Net vega is quote currency for a one-percentage-point volatility move, such as 12% to 13%, with other model inputs locally unchanged. Legs with different expiries and strikes can use different entered flat volatilities, but the tool does not construct a common smile or specify sticky-strike, sticky-delta or surface dynamics.
Net signed model premium treats long option values as positive assets and short option values as negative liabilities under the disclosed model. It is not acquisition cash flow, account equity, liquidation value or accounting fair value because entered trade premiums, bid-ask, collateral, settlement, credit and provider adjustments are not included.
Worked example from the audited fixture
The audited fixture uses EUR/USD spot 1.10000, 4% USD quote-currency continuous rate, 2% EUR base-currency continuous rate and a 365-day basis. It enters three legs: long EUR 100,000 call at 1.12000 with 12% volatility and 180 days; long EUR 50,000 put at 1.08000 with 11% and 90 days; and short EUR 75,000 call at 1.15000 with 13% and 270 days.
The gross base notional is EUR 225,000. Signed theoretical premium totals USD +1,317.73. The first call contributes +47,351.77 base delta units, the put contributes −16,174.31 and the short call contributes −30,822.37.
Net unadjusted spot delta is EUR +355.09 base units. Net gamma is +489,073.53 base units per one full spot unit and net vega is USD +129.64 for a one-volatility-point move. The displayed −355.09 offset is arithmetic only, not a hedge instruction.
How to interpret the result
- Verify every leg belongs to the same base/quote pair and orientation before interpreting any net amount.
- Use net delta as a local model equivalent, not a fixed hedge ratio. Delta changes with spot, time, volatility and market convention.
- Read positive gamma as locally increasing delta when spot rises and negative gamma as the reverse; use full repricing for nontrivial moves.
- Read vega in quote currency for one percentage point, not for a 1.00 absolute-volatility move and not as a forecast of volatility change.
- Review the leg audit because a small net value can hide large offsetting gross exposures, different expiries and concentrated short-option risk.
- Use the price-scenario tool for a specific before-expiry shock and actual entered premiums when the job is scenario P&L rather than local exposure aggregation.
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 broker account, option chain, position feed, bid, ask, volatility surface, yield curve, order, exercise, assignment or settlement data is connected.
- Only plain-vanilla European calls and puts are supported. American, barrier, digital, Asian and other path-dependent structures are excluded.
- Each leg uses one flat entered volatility and constant continuous rates. Smile, skew, term-structure dynamics, jumps and stochastic processes are omitted.
- Greeks are local analytical approximations. Large spot, volatility or time changes require full repricing and can introduce interaction effects.
- Premium-adjusted delta, forward delta, pair-specific ATM rules, contract multipliers, account conversion, margin, collateral and hedge execution are excluded.
- No leg, netting action, spot offset, hedge, volatility, strike, expiry, provider, broker, strategy, signal or trade is recommended.
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 Garman-Kohlhagen pricing, delta, gamma and vega.
- CME Group — Options Analytics: Greeks and IV — Primary-market education reference for interpreting option sensitivities as changing local measures.
- CME Group — Options Premium and the Greeks — Primary-market reference for premium components and delta, gamma and vega concepts.
Frequently asked questions
- It sums signed model premium, unadjusted spot delta, gamma and one-volatility-point vega across entered European call and put legs.
- Version 1.0.0 supports one through twenty legs and withholds an empty or larger portfolio.
- No. Every leg in one calculation must use the same base/quote pair and orientation because the output units are shared.
- It is base-currency units under the model unadjusted spot-delta convention.
- It is quote currency for a one-percentage-point change in the entered annualized volatility, with other inputs locally unchanged.
- Large long and short leg exposures can offset locally while retaining substantial gamma, vega, gap, liquidity and path risk.
- No. It is the arithmetic negative of model net delta and does not account for execution, convention, costs, margin or future delta changes.
- No. It is signed theoretical value under entered assumptions, not acquisition cash flow, executable liquidation value or realized P&L.
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