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Greeks Overview

The Greeks module in Options Chain Features (OCF) provides deterministic, model-ready representations of option risk at both the contract level and the option-chain level.

Scope of the Greeks Module

The Greeks subsystem covers two distinct layers:

  1. Per-option Greeks Black–Scholes Greeks computed for each option contract

  2. Aggregate Exposure Features Chain-level summaries describing how risk is distributed across strikes and deltas

These layers are designed to be composable and independently usable.

Design Philosophy

OCF's Greeks implementation follows a few strict principles:

  • Deterministic inputs only Greeks are computed from spot, strike, time, rate, and mapped volatility and not from option prices.

  • No implied volatility inversion Volatility is mapped from surfaces or historical data, never solved from prices.

Inputs Required

Greeks computation requires:

1. Canonical Option Chain Snapshot

One row per option contract containing:

  • Strike
  • Expiration
  • Call and put tickers
  • Contract size
  • Metadata required for valuation

2. Underlying Snapshot (Single Row)

A single underlying row providing:

  • Spot price
  • Valuation date
  • Risk-free rate
  • Implied volatility surface fields (if available)

Per-Option Greeks

Per-option Greeks are computed using a standard Black–Scholes framework.

For each contract, OCF computes:

  • Price
  • Delta
  • Gamma
  • Vega
  • Theta
  • Charm
  • Vanna
  • Vomma

Each option (call and put) is treated independently.

See Per-Option Greeks for details on inputs, outputs, and volatility mapping.

Aggregate Exposure Features

Aggregate exposure features summarize how Greek risk is distributed across the option chain.

Instead of returning raw position-level data, OCF computes:

  • Total exposure per Greek
  • Delta-weighted exposure moments
  • ATM concentration metrics
  • Directional exposure slopes

These features describe where risk lives in the chain.

See Exposure Features for definitions.

Volatility Mapping

Implied volatility is mapped deterministically using a structured fallback:

  1. Smile interpolation from moneyness surfaces
  2. ATM term structure interpolation
  3. Historical ATM implied volatility

This ensures consistent volatility inputs across calls and puts.

See Volatility Mapping in Per-Option Greeks for full details.

Public APIs

The Greeks module exposes three stable APIs:

API Purpose
per_option_greeks Compute Greeks per contract
exposure_features Compute chain-level exposure features
option_chain_greeks Convenience wrapper combining both

All APIs:

  • Perform no IO
  • Require explicit inputs
  • Return Polars DataFrames

When to Use Greeks in OCF

Typical use cases include:

  • Feature engineering for ML models
  • Regime classification
  • Risk surface analysis
  • Cross-sectional option research
  • Stress and scenario modeling

Next Sections

  • Per-Option Greeks – contract-level computations and volatility mapping
  • Exposure Features – chain-level aggregation and interpretation