FX Volatility Intelligence
FX Vol Surface Builder — Vanna-Volga Smile & Term Structure
Build an implied volatility surface from ATM, risk-reversal, and butterfly quotes — smile, term structure, and per-tenor diagnostics.
Implied Vol Surface Builder — EURUSD
Paste OTC broker quotes for each tenor, or use Auto-fill to pre-populate a model smile. All values in vol points (%). Leave tenors blank to skip.
What are these inputs?
ATM Vol — At-the-money implied volatility. The market's forward-looking estimate of how much the pair will move, annualized. A level of 8% means the market implies ~8% annualized moves.
Risk Reversal (RR) — The vol difference between an OTM call and OTM put at the same delta (e.g. 25Δ call − 25Δ put). It captures directional bias: negative RR = puts are bid (market fears a drop); positive = calls are bid (market expects a rally). Typical G10 range: −2% to +2%.
Butterfly (BF) — The average of the two OTM vols minus ATM: [(25Δ call vol + 25Δ put vol) / 2] − ATM vol. It measures the smile premium — how much more expensive wings are than ATM options, reflecting fat-tail risk. Always positive in real markets. Typical range: 0.05% to 0.50%.
⚠ Auto-fill populates model estimates from the pair's own realized-return distribution — not market quotes. For production-grade pricing, override with your own Bloomberg (FXVOL <GO>), Reuters Eikon, or vol desk quotes. A flat smile (RR=0, BF=0) is unrealistic — all real FX pairs have positive BF and non-zero RR.
| Tenor | ATM Vol %? | 25Δ RR %? | 25Δ BF %? | 10Δ RR %? | 10Δ BF %? |
|---|---|---|---|---|---|
| 1W | |||||
| 1M | |||||
| 3M | |||||
| 6M | |||||
| 1Y | |||||
| 2Y |
What is the model smile based on?
The whole smile is estimated from the pair's own historical daily spot returns — no options-market data is used:
- ATM term structure — a mean-reverting curve between the current EWMA volatility (short end) and the long-run realized volatility (long end). This avoids the collapse you get from raw short-window realized vol, which understates near-dated implied vol.
- Risk-reversal (skew) — the skewness of realized returns is mapped to the 25Δ risk-reversal: a downside-skewed distribution puts a bid on puts (negative RR), an upside-skewed one on calls.
- Butterfly (curvature) — the excess kurtosis of realized returns is mapped to the 25Δ butterfly via a Gram-Charlier smile expansion: the fatter the tails, the more the wings cost relative to ATM. Structurally non-negative, capped at 0.45 vol pts.
Computed once per day at the EOD close. Returns are winsorised so a single bad tick can't dominate the skew/kurtosis, and the daily→tenor scaling uses an empirical ramp rather than i.i.d. aggregation. These are model estimates, not market quotes: override with your own desk quotes for production pricing.
About the vol surface builder
The surface builder turns standard OTC FX option quotes — at-the-money volatility, 25-delta risk reversal, and 25-delta butterfly — into a full implied volatility smile for each tenor from 1 week to 2 years, using the Vanna-Volga method (Castagna–Mercurio). Paste quotes from your broker or terminal, or use auto-fill to pre-populate indicative market levels, then build the surface to see the smile by delta, the ATM/RR/BF term structure, and per-tenor diagnostics including 25Δ call and put vols and outright forwards.
Because 25Δ butterfly quotes are rarely published on free data sources, an optional end-of-day model estimate fills the wing premium from the pair's realized-return tail statistics — always labelled as a model estimate, never passed off as a market quote. The finished surface feeds the Greeks & Scenarios simulator for smile-consistent pricing and risk.
Frequently asked questions
What is the volatility smile in FX options?
The volatility smile is the pattern where out-of-the-money options trade at higher implied volatility than at-the-money options. In FX it reflects two things: fat tails (big moves happen more often than a lognormal model implies), which lift both wings, and directional fear, which tilts one wing above the other. The smile is described in the market by three quotes per tenor: ATM vol, risk reversal, and butterfly.
What is a 25-delta risk reversal?
A 25-delta risk reversal (RR) is the implied vol of a 25Δ call minus the implied vol of a 25Δ put on the same tenor. It measures the skew of the smile — which side the market is paying up for. A negative RR means puts are bid (downside protection in demand); positive means calls are bid. Typical G10 levels run from −2% to +2% in vol points.
What is a butterfly quote in FX options?
The 25-delta butterfly (BF) is the average of the 25Δ call and 25Δ put vols minus the ATM vol. It measures the curvature of the smile — how much more expensive the wings are than the middle, reflecting fat-tail risk. It is almost always positive in real markets, typically 0.05% to 0.50% in vol points for G10 pairs.
What is the Vanna-Volga method?
Vanna-Volga is a practitioner technique for interpolating a full FX volatility smile from just three market quotes (ATM, risk reversal, butterfly). It prices the cost of hedging the second-order Greeks — vanna and volga — that a flat Black-Scholes vol ignores, and adjusts the smile accordingly. It is the standard quick method on FX options desks for building a smile without a full stochastic-vol calibration.
Realized vol computed from daily FX spot history (Twelve Data, with yfinance and FRED fallback). Carry from FRED OECD MEI 3M interbank rates. Positioning from CFTC Traders in Financial Futures (TFF) — free weekly data. Implied vol surface requires user-supplied OTC quotes.
