Options Pricing Documentation

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Comprehensive reference documentation for Options Analysis Suite. The platform exposes 17 institutional-grade pricing models, all 17 Greeks, the full set of dealer-flow analytics (gamma exposure, dealer delta exposure, max pain), and a transparent methodology that documents every data source and assumption. This documentation is organized into three layers: foundational pricing models, market-structure analytics, and a glossary of options-trading terminology. Each page links to the live calculator at /analysis and to per-ticker live data so readers can move from concept to application immediately.

Foundational Pricing Models

The reference set covers the canonical models in production use across institutional trading desks. Black-Scholes is the closed-form starting point: fast, universally understood, and the reference every other model is compared against. Heston adds stochastic volatility for surface-aware pricing. SABR fits per-expiration smiles cleanly. Local Volatility calibrates exactly to the listed surface by construction. Jump Diffusion (Merton, Kou, Bates) handles event risk. Variance Gamma models fat-tailed Lévy returns. Binomial trees and PDE methods handle American exercise. Monte Carlo covers exotics and risk-neutral distributions. FFT is the engine behind every characteristic-function model.

Market-Structure Analytics

The platform extends beyond pricing into structural analytics that reveal how the options market actually behaves. Gamma exposure aggregates per-strike gamma across the full chain to show where dealer hedging flows pin price. Max pain computes the strike at which option holders lose the most: sometimes a gravitational attractor near expiration, sometimes meaningless, depending on regime. Volatility surfaces visualize IV across strike and tenor as a 2D shape, not a scalar. Term structure reveals event pricing through the IV curve. Expected move translates IV into a price-range forecast. Probability distributions turn the surface into the full risk-neutral histogram of outcomes. The pricing model landscape map shows how different models relate, where they disagree, and why those gaps are themselves priced information.

Greeks and Risk Sensitivities

The 17-Greek reference covers first-order risks (delta, gamma, theta, vega, rho), second-order cross-sensitivities (vanna, charm, vomma, veta, color), and the higher-order Greeks (speed, zomma, ultima) used in vol-arbitrage risk management. Greeks are computed analytically from Black-Scholes by default and via Fourier or PDE methods for the smile-aware models. The Greeks history view tracks aggregate delta, gamma, and vega exposure over time per ticker.

Glossary and Conventions

The options trading glossary defines 71 core terms (implied volatility, volatility skew, dealer hedging, the leverage effect, risk-neutral probability, and others) each with a short definition and a link to the relevant deep-dive. For users new to options or new to OAS, the glossary is the right starting point. The Charts & Analytics hub is the visual companion: every concept has a chart that surfaces the analytic on real data.