Options
Mock-up. Gold 1-month implied volatility is 17.9% and 2-month 19.9%; the 1-month risk reversal is -0.1 vol points
Mock-up: Bloomberg only has GLD implied volatility at 1M and 2M, for the 10, 25, 50 and 75 delta calls and puts. The 75 delta call is the same point as the 25 delta put (and the reverse), so each tenor has 5 points.
A full term structure and a real surface need more tenors (3M, 6M, 12M) in the database.
Skew, smile and contango
Pick a chart; the explanation under the selector changes with it. Lines in volatility points. Orange: XAU (right axis, log).
Skew = σ(call 25Δ) − σ(put 25Δ), for 1M and 2M. σ is the Bloomberg implied volatility of a GLD option whose delta is +0.25 (call) or −0.25 (put): the call 25Δ has its strike above spot and the put 25Δ below it, at about the same distance. Positive: upside calls cost more than downside puts, so the market pays more for a rally than for protection against a fall. Negative: the usual equity-style skew, puts are bid.
Smile = [σ(call 25Δ) + σ(put 25Δ)] / 2 − σ(ATM), for 1M and 2M, where ATM is the 50Δ option. It measures the curvature of the smile: how much more the two wings cost than the at-the-money option. Positive and rising: the market prices bigger moves in either direction (fat tails). Near zero: a flat smile.
Contango = σ(2M) − σ(1M) at each delta point: put 10Δ, put 25Δ, ATM, call 25Δ and call 10Δ (ATM in bold). Positive: longer options carry more volatility, the normal upward term structure. Negative: the curve is inverted, short-dated options cost more because the market expects the stress to be near.
These are the quoting conventions of FX options (Reiswich and Wystup, 2010, "A Guide to FX Options Quoting Conventions", Journal of Derivatives). Days with a point printed at more than 3 times that day's median are dropped (2012-07-19, 2026-03-13 and 2026-03-16).
Implied volatility surfaces
Left: today, implied volatility by delta (puts on the left, calls on the right) and tenor (1M and 2M; with two tenors it is a ribbon). Right: pick a series to see how it moved week by week over the last two years. Drag to rotate.
Implied volatility of each delta point at 1M, one line per week over the last two years.
Implied volatility of each delta point at 2M, one line per week over the last two years.
σ(2M) − σ(1M) at each delta point, weekly. Red below zero: the curve is inverted, short-dated options cost more.