FX Risk Reversal & Butterfly Calculator
Convert between ATM volatility plus risk-reversal and simple butterfly quotes, and the corresponding call- and put-wing volatilities. The delta selection is a quote label only: this tool performs algebraic volatility conversion without solving strikes, prices or a volatility smile.
Choose a volatility quote conversion
Use volatility percentages and volatility-point differences. A risk reversal of +1.2 means call volatility minus put volatility equals +1.2 points.
Simple RR and butterfly conversion
Derived from FX Option Quote Conventions model 1.0.0.
How simple FX risk reversal and butterfly quotes convert
A risk reversal records the difference between call-wing and put-wing implied volatility at a stated delta label. A positive RR under this page convention means the call wing has higher volatility than the put wing; a negative value means the put wing is higher.
The simple butterfly records how far the arithmetic average of the two wing volatilities sits above or below ATM volatility. Combining ATM, RR and BF produces two linear equations, allowing the call and put wing volatilities to be recovered directly.
The reverse mode accepts ATM, call-wing and put-wing volatility and collapses them into RR and simple BF. Both directions use volatility percentage points, not decimals: 12, 13.1 and 11.9 mean 12%, 13.1% and 11.9%.
The 10-delta or 25-delta selector labels the quote set but is not used in the arithmetic. To associate those wing volatilities with strikes, a user must apply the correct pair-specific delta convention, rates, time and a smile-consistent procedure outside this route.
The term butterfly is not universal. Market participants may quote a market strangle whose option premium or vega relationship must be solved rather than averaged. This calculator deliberately calls its output a simple average-volatility butterfly.
Three volatility points do not create a complete volatility surface. Interpolation across strike or delta, extrapolation, expiry structure, calendar consistency and arbitrage controls require a governed smile or surface construction method.
Worked example from the audited fixture
The audited fixture enters 25-delta wings, ATM volatility 12.0%, risk reversal +1.2 volatility points and simple butterfly +0.5 volatility points.
Call wing volatility is 12.0 + 0.5 + 1.2 ÷ 2 = 13.1%. Put wing volatility is 12.0 + 0.5 − 1.2 ÷ 2 = 11.9%.
The average wing volatility is 12.5%, which is 0.5 points above ATM. Collapsing 13.1% and 11.9% returns RR +1.2 and BF +0.5.
How to interpret the result
- Name the convention: these outputs use a simple average-volatility butterfly, not an unspecified market butterfly.
- Read positive RR as call volatility above put volatility under the page sign convention; verify a counterparty uses the same sign.
- Treat 10-delta or 25-delta as a label only. This route does not determine the associated strikes.
- Check that every input uses volatility percentage points rather than decimal volatility or option premium.
- Reject converted nonpositive wing volatilities as inconsistent input rather than clipping them to zero.
- Use a separate governed procedure for vega weighting, smile interpolation, arbitrage checks and option pricing.
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, ATM quote, risk reversal, butterfly, strike, premium, rate curve or market timestamp is connected.
- Only the disclosed simple average-volatility BF convention is calculated; market-strangle and vega-weighted conventions are excluded.
- The 10-delta and 25-delta choices are labels and do not change the algebra or solve strikes.
- ATM definitions, spot versus forward delta, premium adjustment and pair-specific quotation rules are not inferred.
- The output is not an interpolated, calibrated or arbitrage-free volatility smile or surface.
- No volatility quote, strike, 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.
- Reiswich and Wystup — FX Volatility Smile Construction — Research paper defining ATM, risk-reversal and butterfly quote relationships and discussing convention choices.
- FX Options Pricing with Market Conventions — Peer-reviewed treatment of delta, ATM and volatility-smile quotation conventions.
- QuantLib — BlackDeltaCalculator Source — Implementation reference showing why delta and ATM conventions must be explicit before mapping volatility quotes to strikes.
Frequently asked questions
- On this page it is call-wing volatility minus put-wing volatility at the selected delta label.
- BF equals the average of call and put wing volatility minus ATM volatility.
- Not necessarily. Market-strangle or vega-weighted conventions can require option pricing and a different solution.
- No. The selected 10-delta or 25-delta value is a quote label only on this route.
- No. Strike conversion requires spot, rates, time, volatility and the correct delta convention.
- RR and BF are differences between volatility percentages, so +1.2 means +1.2 percentage points of volatility.
- No. It provides three quote points without interpolation, extrapolation or arbitrage controls.
- The calculator only reports relative wing volatility. It does not infer positioning, direction, probability or a trade signal.
Separate quote conversion from strike and premium calculations
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