Methodology
Free to readHow Skew Deconstruction Works
The fit behind the three numbers — how the IV curve is reduced to Level, Slope, and Curvature, and how those tie back to the Nations volatility suite.
The deconstruction borrows its idea from principal-component analysis of yield curves, where a whole term structure collapses into a few dominant factors — level, slope, and curvature. The same three factors describe an implied-volatility curve at a single tenor. Here's exactly how each is computed.
The fit
For a chosen tenor, the tool takes every matched call/put strike pair within ±40% of spot and fits a weighted quadratic of implied volatility on log-moneyness, x = ln(K/S):
IV(x) ≈ β₀ + β₁·x + β₂·x²
Fit by weighted least squares (open interest as the weight, so liquid strikes count more). The three coefficients are the three components; whatever the curve does that this can't capture is residual.
The fit: each matched strike’s IV is a point against log-moneyness x = ln(K/S). A least-squares parabola is fit through them; its three coefficients become Level, Slope, and Curvature.
Level
Level is the overall height of the surface — the open-interest-weighted average IV across all matched strike pairs within ±40% of spot. It's the analog of the parallel-shift factor in fixed-income PCA, and the dominant driver of variance in the IV surface over time. When the whole curve lifts, Level lifts. This is the same quantity Nations VolDex® measures at-the-money.
Level is β₀ — the fitted IV at the money (x = 0). It is the height of the whole surface, the same quantity VolDex® measures.
Slope
Slope is β₁ — the first-order coefficient, the linear tilt of IV across log-moneyness. In equities it is almost always negative: put options trade at higher IVs than calls at equivalent distance from spot, because demand for downside protection structurally exceeds demand for upside participation. Slope becomes less negative (skew flattens) during realized rallies and more negative (steepens) during stress. The put-vs-call tilt Slope captures is exactly what drives RiskDex® — the ratio of PutDex® to CallDex® at equivalent deltas.
Slope is β₁ — the tilt of the fit at the money. Negative β₁ is the normal equity put-skew; it drives RiskDex®.
Curvature
Curvature is β₂ — the coefficient on x², the second-order "smile." It measures how bid the wings are relative to the straight-line tilt. High curvature means tail risk is priced at a premium beyond what the linear skew predicts; it is the primary driver of the price of far-OTM options (both puts and calls) in excess of their intrinsic skew adjustment. Curvature is the engine behind TailDex® — the normalized price of the ~3-sigma OTM put. When curvature rises here, TailDex® rises.
Curvature is β₂ — how far the fit bows away from the straight line, i.e. the smile. It rises when the wings are bid; it drives TailDex®.
Residuals
After extracting Level, Slope, and Curvature, the residuals are the IV deviations the three components don't explain — idiosyncratic, strike-level mispricing. Large residuals at specific strikes often mean a supply/demand imbalance (a concentration of open interest at one strike) or a data anomaly. They're the noise around the signal, and occasionally a signal of their own.
Live components come from the current options chain. The historical series uses return-based proxies derived from daily closing returns of the underlying. The risk-free rate is the 13-week U.S. Treasury bill, updated daily; dividend yield is assumed 0%, so dividend-paying names can show minor distortion. Approximate tenors resolve to the nearest listed expiration at or beyond the target.
Residuals are the gaps between each strike’s actual IV and the fitted curve — the part the three components don’t capture.
How it maps to the Nations suite
The deconstruction is the microscope behind three Nations indexes: Level ↔ VolDex® (the at-the-money height), Slope ↔ RiskDex® (the put-vs-call tilt), Curvature ↔ TailDex® (the wing premium). Read the components and you understand precisely what those headline indexes are built from — and because RiskDex® and TailDex® are published indexes, you can alert on the Slope and Curvature regimes directly.
The methodology is free. The full historical component series — Level, Slope & Curvature tracked over time — is an Everything-tier capability; single-name deconstruction needs ETF + Equities.
See plans →Educational content from Nations Indexes. VolDex®, RiskDex®, PutDex®, CallDex®, and TailDex® are registered marks of Nations Indexes. Nothing here is investment advice.