Financial Math Library

A Python library for pricing derivatives, simulating stochastic processes, and analyzing fixed income instruments.

Features

• Options Pricing

  • Black-Scholes analytical pricing
  • Heston stochastic volatility model
  • Monte Carlo simulation
  • Binomial/trinomial trees
  • Implied volatility calculation

• Stochastic Processes

  • Arithmetic Brownian Motion (ABM)
  • Geometric Brownian Motion (GBM)
  • Cox-Ingersoll-Ross (CIR)
  • Ornstein-Uhlenbeck (OU)
  • Vasicek
  • Jump diffusion (Merton)

• Fixed Income

  • Bond pricing and yield curve tools

• Portfolio

  • Risk and performance metrics

Project Structure

fixed_income/
    fixed_income.py        # Fixed income pricing and analytics

options/
    iv.py                  # Implied volatility solver
    option.py              # Option contract definitions

portfolio/
    metrics.py             # Portfolio risk/performance metrics

pricing/
    black_scholes.py       # Black-Scholes model
    heston.py               # Heston stochastic volatility model
    monte_carlo.py          # Monte Carlo pricing engine
    trees.py                 # Binomial/trinomial tree pricing

processes/
    abm.py                  # Arithmetic Brownian Motion
    cir.py                    # Cox-Ingersoll-Ross process
    gbm.py                   # Geometric Brownian Motion
    jump_diffusion.py        # Jump diffusion process
    ou.py                      # Ornstein-Uhlenbeck process
    vasicek.py                # Vasicek interest rate model

testing.ipynb              # Example usage and validation notebook

Installation

pip install finmat

Usage

See testing.ipynb for example workflows, including:

• Pricing European options with Black-Scholes and comparing to Monte Carlo
• Simulating asset paths with GBM, CIR, and jump diffusion processes
• Calibrating the Heston model to market data
• Computing implied volatility surfaces
• Evaluating fixed income instruments and portfolio metrics

Requirements

• Python 3.8+
• NumPy
• SciPy
• matplotlib (for notebook visualizations)

License

This project is licensed under the MIT License - see the LICENSE file for details.