FX Volatility Quoting Conventions

Order a coffee at most cafes and you say "small," "medium," "large" — not weight in grams. FX options traders quote vol in a similarly convenient shorthand: not by strike price, but by delta, because a dollar strike is meaningless without knowing spot and tenor, while "the 25-delta option" means roughly the same thing (about a 25% chance of finishing in the money) for any pair or spot level. Three delta-referenced numbers per maturity — ATM, risk reversal, butterfly — are the entire quoting system.

The three quotes, defined

ATM vol is the implied vol of the at-the-money option. Risk reversal (RR) is the vol difference between an OTM call and an OTM put at the same delta magnitude:

$$\text{25d RR} = \sigma(25\Delta\ \text{call}) - \sigma(25\Delta\ \text{put})$$

In words: the vol of the option 25% likely to be exercised on the call side, minus the same on the put side. Positive RR means calls are bid up relative to puts; negative RR, the more common sign for most pairs, means puts (downside protection) are bid up. Butterfly (BF) is how much the average of the two OTM vols sits above the ATM vol:

$$\text{25d BF} = \frac{\sigma(25\Delta\ \text{call}) + \sigma(25\Delta\ \text{put})}{2} - \sigma_{\text{ATM}}$$

In words: it measures the smile's curvature — how much richer the wings are than the middle, on average, regardless of which wing is richer (that asymmetry is RR's job).

Worked example 1 — reconstructing the smile from quotes

A desk quotes EUR/USD 3-month vols as: ATM = 8.0%, 25d RR = -1.2%, 25d BF = 0.4%. Solve for the two OTM vols. From BF: $\sigma(25\Delta C) + \sigma(25\Delta P) = 2 \times (0.4\% + 8.0\%) = 16.8\%$. From RR: $\sigma(25\Delta C) - \sigma(25\Delta P) = -1.2\%$. Adding and halving: $\sigma(25\Delta C) = (16.8\% - 1.2\%)/2 = 7.8\%$. Subtracting: $\sigma(25\Delta P) = 16.8\% - 7.8\% = 9.0\%$. Check: RR $= 7.8\% - 9.0\% = -1.2\%$ ✓. The negative RR confirms puts are bid richer than calls, typical where the market fears depreciation more than appreciation.

Worked example 2 — reading a sign flip

A different pair, AUD/JPY, quotes ATM = 11%, 25d RR = +2.0%, 25d BF = 0.6%. Following the same steps: $\sigma(25\Delta C) + \sigma(25\Delta P) = 2 \times (0.6\% + 11\%) = 23.2\%$, and the difference is $+2.0\%$, so $\sigma(25\Delta C) = (23.2\% + 2.0\%)/2 = 12.6\%$ and $\sigma(25\Delta P) = 23.2\% - 12.6\% = 10.6\%$. Here the positive RR means calls (AUD strength) are the richer wing — a flag to a trader that hedging demand has shifted, worth a second look rather than taking at face value.

What this means in practice

Every FX options desk builds its whole surface, tenor by tenor, from exactly these triplets — it's how brokers publish quotes and how vanna-volga and other smile-construction methods (see vanna-volga method) take their three benchmark inputs. Reading RR and BF directly tells a trader the smile's skew and convexity without ever looking at a strike-vs-vol chart.

Practice

1. A desk quotes ATM = 12%, 10d RR = -2.5%, 10d BF = 0.9%. Solve for the 10-delta call and put vols.
2. If a currency pair's 25d RR flips from -1.0% to +0.5% over a week with ATM roughly unchanged, what does that say about which side of the smile the market is now paying more for?