Options Pricing Library

A Python library for option pricing, Greeks, strategies, volatility modeling, risk management, calibration, and backtesting — with clean implementations of classic models and a full suite of demo notebooks.

This project is designed as an educational and demonstrational toolkit for quantitative finance.

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Theory Reference

For background on the Central Limit Theorem (CLT), Brownian Motion, Ito's Lemma, and the Black–Scholes model:

notebooks/00_Theory-CLT-ITO-BS.ipynb

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Features

• Core pricing models

  • Black–Scholes closed form (with dividend yield q)
  • Binomial Tree (European & American)
  • Monte Carlo simulation
  • Finite Difference PDE solvers (explicit / implicit / Crank–Nicolson)
  • American options via Longstaff–Schwartz (LSMC)

• Stochastic volatility models

  • Heston via COS method (fast & stable)
  • SABR (Hagan asymptotic IV) with calibration in IV- and price-space
  • Rough models: rBergomi and Rough Heston (MC), parallelizable

• SVI volatility surfaces

  • Arbitrage-aware SVI parameterization and fitting
  • Calendar stitching to reduce cross-maturity arbitrage
  • Visualization utilities (smiles, 2D/3D surfaces, ATM term structure)

• Greeks & sensitivities

  • Delta, Gamma, Vega, Theta, Rho (supports dividend yield q)
  • Vanna & Volga; pathwise and finite-difference Greeks for MC

• Strategies and risk

  • Standard strategies (spreads, straddles, collars, calendars)
  • Payoff diagrams; portfolio aggregation and stress grids
  • VaR/ES (historical and Monte Carlo) and P&L attribution

• Barriers and digitals

  • Barrier pricing via MC with Brownian-bridge correction
  • Digital cash and asset binaries under Black–Scholes

• Data & utilities

  • Optional yfinance helpers for stock/chain data (see data/)
  • Time-to-maturity, rolling vol, calendars, and helpers

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Notebooks Map

• 00 Theory: CLT, Ito, Black–Scholes
• 01–07 Core demos: Black–Scholes, Binomial, Monte Carlo, Finite Difference, Greeks, Strategies
• 08–10 Backtesting and portfolio risk (uses optional yfinance)
• 11 American: LSMC and binomial
• 12 Heston pricing; 13 Heston calibration (forward-based, vega-weighted)
• 14 SABR calibration (IV- and price-space)
• 15 SVI surface fitting and calendar stitching
• 16 Hurst exponent estimators; 17 Delta hedging
• 18 Barriers (MC + Brownian bridge)
• 19 Rough models; 20 Rough calibration
• 21 Multi-maturity calibration (Heston, rBergomi, Rough Heston)
• 99 Parallel calibration benchmark