Implied Volatility Term Structure Features¶

Overview¶

The Term Structure feature block extracts time-dimension structure from ATM implied volatility across maturities. It operates on daily, canonical underlying data and uses only ATM implied volatility levels at different tenors. No option-level data, pricing models, or forward curves are required.

These features describe:

Whether volatility is upward or downward sloping
The relative steepness of the curve
Simple curvature proxies
Forward variance implied by adjacent maturities

Required Input Columns¶

The following columns must be present in the canonical underlying daily table:

Column	Description
`iv_30_m100`	30-day ATM implied volatility (100% moneyness)
`iv_60_m100`	60-day ATM implied volatility (100% moneyness)

If either column is missing, the feature block raises an error.

Tenor Conventions¶

Tenors are interpreted as calendar days, converted to year fractions:

Tenor	Year Fraction
30D	30 / 365
60D	60 / 365

All computations assume implied volatilities are expressed in decimal form.

Produced Feature Columns¶

Term Structure Shape¶

Feature	Description
`iv_term_slope_30_60`	Difference between 60D and 30D ATM IV
`iv_term_ratio_30_60`	Ratio of 60D to 30D ATM IV

These features indicate whether the volatility curve is: - Upward sloping (longer-dated IV > shorter-dated IV) - Inverted (short-term IV elevated relative to longer-term)

Curvature Proxy¶

Feature	Description
`iv_term_curvature_30_60`	Simple curvature proxy between 30D and 60D ATM IV

This acts as a minimal curvature indicator when only two tenors are available.

Forward Variance¶

Feature	Description
`iv_fwd_var_30_60`	Implied forward variance between 30D and 60D

Forward variance is computed by comparing the total variance implied by a longer-dated option with that implied by a shorter-dated option, after scaling each by its respective time to maturity. The implied volatilities at the money for the short and long maturities are combined with their year-fraction tenors to extract the portion of variance that lies strictly between the two maturities. In doing so, this measure isolates the incremental variance implied beyond the shorter horizon, providing a clean view of the market’s expectation of variance over the forward period rather than over the entire life of the longer-dated option.

Masking Rules¶

All term structure features are masked (null) when either source IV is missing:

iv_30_m100
iv_60_m100

This prevents partial or invalid term structure signals.

How to Call This Feature Block¶

Recommended (Public API)¶

from ocf.features.api import term_structure_features

features = term_structure_features(
    underlying_daily,
)

This validates the canonical schema and enforces a stable output contract.

Direct Builder Access (Advanced)¶

from ocf.features.term_structure import build_term_structure_features

features = build_term_structure_features(
    underlying_daily,
)

This assumes canonical inputs and skips schema validation.

As Part of the Composite Feature Set¶

from ocf.features.api import underlying_features

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

Or combined with other volatility features:

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

Notes¶

Features are daily and fully causal
No forward curve construction is assumed
Only adjacent tenor information is used