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 both an educational toolkit and a reusable research library for quantitative finance.

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Theory Reference

For detailed explanations of the fundamental theories used in this package, including the Central Limit Theorem (CLT), Brownian Motion, Itô’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
  • 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 model via COS method (fast & stable)
  • Batch multi-strike Heston pricer (vectorized COS)
  • SABR model (Hagan asymptotic IV)
  • Calibration routines (price- and IV-space, vega-weighted, forward-based)
  • Synthetic surface generation & recovery tests

• Greeks & Higher-Order Sensitivities

  • Δ, Γ, Vega, Θ, ρ
  • Vanna & Volga
  • Pathwise & finite-difference Greeks for Monte Carlo

• Option Strategies

  • Vanilla legs (long/short calls & puts)
  • Spreads (bull, bear, butterfly)
  • Combinations (straddle, strangle, collar, covered call, calendars)
  • Payoff diagram visualizations

• Volatility Tools

  • Implied volatility solver
  • Surface construction (strike, maturity, moneyness)
  • Volatility smile fitting and diagnostics

• Risk & Portfolio Analytics

  • Aggregated Greeks
  • Scenario analysis (Taylor vs full revaluation)
  • P&L attribution
  • Stress testing grids
  • Historical & Monte Carlo VaR/ES

• Backtesting

  • Constant σ vs realized σ comparisons
  • Strategy rolling backtests
  • Free-float weighted equity indices
  • Return correlation heatmaps

• Data Utilities

  • yfinance integration for stock data & option chains
  • Forward/discount inference via put–call parity regression
  • Realized volatility estimators
  • Time-to-maturity helpers
  • Calendar rolling utilities