VEGA FIELD GUIDE · 11 · VOLATILITY
Reading the volatility surface
The surface is the whole neighborhood. Term structure is one street and skew is another. Put them together and you can see where the market has concentrated variance across both price and time.
A surface maps implied volatility across maturity and moneyness or delta.
Log-moneyness and total variance provide stable coordinates for comparison and interpolation.
Normalized sigma nodes make surfaces comparable across symbols with different spot prices and volatility levels.
From chain rows to a research surface
An option chain arrives as discrete strikes and expirations. A research surface organizes those observations into comparable coordinates. Vega provides tenor and delta views for intuitive reading, plus normalized log-moneyness and total-variance nodes for robust historical and cross-sectional analysis.
The goal is a coherent map that preserves the market’s shape and flags areas supported by weak quotes. A colorful grid is easy to draw. A trustworthy grid requires filtering, interpolation discipline, and clear labels.
Coordinates that travel well
Raw strike is tied to the stock price. Log-moneyness uses strike relative to the forward price, which lets a $20 stock and a $500 stock share the same coordinate system. Delta is intuitive for selecting tradable wings, though it also depends on the model and the volatility being solved.
Sigma nodes express distance in units of the market’s expected standard deviation. A minus-one-sigma point sits near a representative downside move for that tenor. Vega includes short and long tenors such as 7 and 180 days and normalized wing nodes so shapes can be compared across the universe.
k = ln(K / F_T), where K is strike and F_T is the maturity-matched forwardTotal variance improves the map
Total variance combines volatility level and time. It is the natural object for interpolating between maturities and computing forward variance. A smooth annualized-IV chart can hide a problem that becomes obvious when total variance falls with maturity.
Static-arbitrage checks look for coherent behavior across strike and time. Calendar consistency, convex option prices across strike, monotone call prices, and sensible wing behavior all contribute to a quality grade. Badges should describe evidence, never decorate it.
w(k,T) = IV(k,T)^2 x TSparse wings and unsupported tenors deserve an empty cell or an extrapolation label. A zero can imply an economically meaningful observation.
Worked example: normalize a 30-day wing
Let spot and the 30-day forward both equal $100. A $90 strike has log-moneyness ln(90 / 100) = -0.105. If its IV is 35%, total variance is 0.35² x 30 / 365 = 0.0101.
With 35% as a local scale, one standard deviation over 30 days is about 35% x sqrt(30 / 365) = 10.0%. Approximate one-sigma price nodes are $100 x exp(-0.100) = $90.48 and $100 x exp(0.100) = $110.52. The $90 strike lands close to the downside one-sigma node, which makes its wing value easy to compare with another symbol’s normalized surface.
| Quantity | Calculation | Value |
|---|---|---|
| Log-moneyness | ln(90 / 100) | -0.105 |
| 30-day total variance | 0.35² x 30 / 365 | 0.0101 |
| One-sigma price range | 100 x exp(plus or minus 0.100) | $90.48 to $110.52 |
A five-minute Surface Lab routine
- Start with the overview and locate the richest tenor and wing by color and value.
- Check the current IV against its historical percentile bands and realized-volatility cone.
- Open forward volatility to isolate the expensive time window.
- Review node quality, quote width, open interest, valid deltas, and any interpolation or extrapolation label.
- Add peer symbols on a shared scale, then open the chain or calculator from the research action.
Explore the full volatility map
Inspect smiles, forwards, distributions, normalized nodes, quality gates, and peer overlays inside symbol research.