FX Option Delta-to-Strike Calculator
Solve the strike whose Garman-Kohlhagen call or put has one entered absolute unadjusted spot delta. The tool uses entered spot, two continuously compounded currency rates, annualized volatility and time, while explicitly excluding forward and premium-adjusted delta conventions.
Enter one unadjusted spot-delta target
Enter the absolute delta percentage, such as 25 for a 25-delta wing. The selected call receives positive signed delta and the selected put receives negative signed delta.
Unadjusted spot-delta strike
Derived from FX Option Quote Conventions model 1.0.0.
How unadjusted spot delta is converted to strike
FX option delta is convention-dependent. This route fixes one narrow definition: unadjusted spot delta. Under Garman-Kohlhagen, call spot delta is positive and put spot delta is negative after applying the base-currency discount factor.
The input is an absolute percentage for convenience. Entering 25 means a +0.25 target for a call or a −0.25 target for a put. The result panel shows both the target and achieved signed values so the option side cannot be hidden by the absolute input.
As strike rises, an otherwise identical call delta falls while put delta becomes more negative. The calculator searches strike in logarithmic space and repeatedly reprices the option until the selected delta matches the entered target.
The largest attainable absolute unadjusted spot delta is constrained by the base-currency discount factor. A target equal to or above that bound is rejected because no finite strike under this convention can reproduce it.
Spot delta is not interchangeable with forward delta because forward delta removes a discounting relationship. Premium-adjusted delta also changes the expression by accounting for premium, and some currency pairs use different market conventions by tenor.
The volatility input remains flat and entered. A professional delta-to-strike conversion often depends on a smile in which volatility itself changes by delta or strike. This page solves a self-consistent constant-volatility case only.
Worked example from the audited fixture
The audited fixture enters EUR/USD spot 1.10000, 4% USD quote-currency rate, 2% EUR base-currency rate, 12% annualized volatility and 180 days on a 365-day basis.
For a 25-delta call under unadjusted spot delta, the solved strike is 1.17928400 and the achieved delta rounds to +25.0000%. Strike is 107.2076% of spot.
The corresponding 25-delta put strike is 1.05394501 with achieved delta −25.0000%. The same inputs have a continuous-rate forward of 1.11090299.
How to interpret the result
- State the result as an unadjusted spot-delta strike. Omitting the convention can make a precise number misleading.
- Confirm call versus put. The input is absolute, but the economic delta sign and solved strike differ by option side.
- Check whether the real quote uses spot, forward, premium-adjusted spot or premium-adjusted forward delta before comparing strikes.
- Treat the entered volatility as a scenario. A smile-consistent strike may require iteration with the market volatility at that delta.
- Use the residual only as a numerical convergence check, not evidence that the convention matches a dealer quote.
- Verify expiry cut, spot date, delivery, rate curves and premium currency independently for a real contract.
Which FX option quote-convention tool answers which question?
These tools share one governed model layer but solve different inverse problems. Premium inversion finds volatility, delta inversion finds strike, and RR/BF conversion rearranges volatility quotes without pricing an option.
| Tool | Required entered data | Output | Hard boundary |
|---|---|---|---|
| Implied volatility | Premium plus spot, strike, two rates and time | One constant volatility | Does not build a surface |
| Delta-to-strike | Spot, two rates, volatility, time and delta | One strike | Unadjusted spot delta only |
| Risk reversal & butterfly | ATM plus RR/BF or two wing volatilities | Volatility quote conversion | Simple average BF; no strikes |
Assumptions and limitations
- No option chain, delta quote, volatility surface, rate curve, broker account, order or contract record is connected.
- Only unadjusted spot delta is supported. Forward and premium-adjusted variants are withheld.
- ATM delta-neutral, ATM forward, ATM spot and other ATM strike conventions are not calculated.
- The underlying valuation assumes a European plain-vanilla option, constant volatility and constant continuously compounded rates.
- Smile calibration, interpolation, vanna-volga adjustments, stochastic models, liquidity and dealer adjustments are excluded.
- No strike, delta, volatility, option, hedge, provider, broker, strategy, signal or trade is recommended.
Sources and methodology
The arithmetic is independently fixture-tested. These primary and implementation references define the formulas and convention distinctions; they do not verify an entered premium, quote, contract, provider or market timestamp.
- QuantLib — BlackDeltaCalculator Source — Open-source implementation distinguishing spot, forward and premium-adjusted FX delta conventions and strike inversion.
- QuantLib — FX Black Delta Calculator Documentation — API documentation for delta types, ATM types and strike-from-delta behavior.
- FX Options Pricing with Market Conventions — Peer-reviewed description of FX delta conventions and their effect on strike and volatility quoting.
Frequently asked questions
- Version 1.0.0 uses unadjusted spot delta only.
- It makes common 10-delta and 25-delta entry simple; the tool assigns positive sign to calls and negative sign to puts.
- No. Spot, rates, volatility, time, option side and delta convention all affect the strike.
- Unadjusted spot delta is bounded by the base-currency discount factor, so some targets have no finite strike.
- No. Premium-adjusted spot and forward delta are explicitly outside version 1.0.0.
- No. It uses one entered constant volatility and does not calibrate or interpolate a surface.
- No. It is model arithmetic under entered assumptions and no dealer quote is connected.
- No. The page does not assess suitability, pricing, liquidity, hedge objectives or expected returns.
Separate delta convention from premium and smile arithmetic
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