Implied Volatility Skew & Smile Features¶

Overview¶

The Skew & Smile feature block extracts cross-sectional shape information from implied volatility surfaces expressed in moneyness space. It operates on daily canonical underlying data containing implied volatility smiles at fixed tenors (e.g. 30D, 60D), and summarizes:

ATM implied volatility
Put and call wing skew
Risk reversals and butterflies
Smile slope and curvature

No option-level data, delta surfaces, or pricing models are required.

Required Input Columns¶

This block requires moneyness-based implied volatility columns using the following naming convention:

iv_<TENOR>_m<MONEYNESS>

Where: - <TENOR> is in calendar days (e.g. 30, 60) - <MONEYNESS> is expressed as a percentage of spot

Example Required Columns¶

For a 30-day surface: - iv_30_m90 → 90% moneyness IV - iv_30_m95 - iv_30_m100 - iv_30_m105 - iv_30_m110

For a 60-day surface: - iv_60_m90 - iv_60_m95 - iv_60_m100 - iv_60_m105 - iv_60_m110

At least three moneyness points per tenor are required to compute smile geometry.

Moneyness Interpretation¶

Moneyness is defined as:

Moneyness = K/S

Where: - K is the strike - S is the spot price

Moneyness < 1.0 → put wing
Moneyness = 1.0 → ATM
Moneyness > 1.0 → call wing

Produced Feature Columns¶

All features are computed per tenor (currently 30D and 60D).

ATM Implied Volatility¶

Feature	Description
`iv_<tenor>_atm`	Implied volatility closest to ATM (moneyness ≈ 1.0)

Wing Skew¶

Feature	Description
`iv_<tenor>_put_skew`	Mean put-wing IV − ATM IV
`iv_<tenor>_call_skew`	Mean call-wing IV − ATM IV

These measure asymmetry of implied volatility around ATM.

Risk Reversal & Butterfly¶

Feature	Description
`iv_<tenor>_rr`	Call-wing IV − Put-wing IV
`iv_<tenor>_bf`	Butterfly: ½(call + put) − ATM

Interpretation: - Risk reversal captures directional skew - Butterfly captures smile convexity around ATM

Smile Geometry¶

Feature	Description
`iv_<tenor>_smile_slope`	Linear slope of IV vs moneyness
`iv_<tenor>_smile_curvature`	Quadratic curvature of IV vs moneyness

These are estimated via polynomial fits:

Slope: first-order fit
Curvature: second-order coefficient

They provide a model-free geometric summary of the smile.

Masking Rules¶

For a given tenor, all features are null if fewer than three valid moneyness IVs are available. Individual components (RR, BF) are masked if either wing is missing. This ensures stability and avoids extrapolation.

How to Call This Feature Block¶

Recommended (Public API)¶

from ocf.features.api import skew_smile_features

features = skew_smile_features(
    underlying_daily,
)

This validates the canonical schema and ensures stable outputs.

Direct Builder Access (Advanced)¶

from ocf.features.skew_smile import build_skew_smile_features

features = build_skew_smile_features(
    underlying_daily,
)

This assumes inputs are already canonical.

As Part of the Composite Feature Set¶

from ocf.features.api import underlying_features

features = underlying_features(
    underlying_daily,
    include=["skew_smile"],
)

Or combined with other volatility features:

features = underlying_features(
    underlying_daily,
    include=["iv", "skew_smile", "term_structure"],
)

Notes¶

Features are computed independently per day
No interpolation or smoothing is applied
Smile geometry is purely cross-sectional