The volatility surface
Skew, curvature and term structure from four parameters.
Equity options do not trade at one volatility across strikes. Demand for downside protection is persistent and one sided, so out of the money puts trade above equidistant calls. A venue pricing every strike from a single number misprices its own wings, and a margin engine built on that surface cannot be trusted with collateral.
Parameterisation
Log moneyness is normalised by the square root of tenor, which holds the shape of the smile stable as expiry varies instead of letting it flatten mechanically.
| Parameter | Value | Effect |
|---|---|---|
| β skew | −0.12 | puts richer than calls |
| γ curvature | 0.35 | a smile rather than a line |
| term slope | 0.04 | per log unit of tenor about 30 days |
| clamp | [0.02, 4] | no strike can return a nonsense volatility |
Measured shape
The surface returns 35.41% at K = 85, 30.00% at the money and 30.74% at K = 115. Downside is richer than upside as required, and upside sits slightly above the at the money level because the curvature term dominates the skew term once |k| is large. This is a smile with a negative tilt, which is the correct shape for single name equity.
Skew and curvature are constants rather than fitted to traded prices. Adequate for a testnet, inadequate for a venue carrying real risk, where the surface should be fitted continuously and the margin engine should consume the fitted surface.