cantaro86/Financial-Models-Numerical-Methods
Financial Models Numerical Methods
This project is a quantitative finance library providing implementations of numerical methods for financial engineering. It focuses on derivative pricing, portfolio optimization, stochastic simulation, and volatility calibration.
The library includes tools for calculating option values using Monte Carlo simulations, binomial trees, and Fourier inversion. It provides a framework for fitting volatility smiles to market data and a simulation engine for generating asset price paths via geometric Brownian motion and jump-diffusion models.
The codebase covers broader numerical analysis capabilities, including solvers for partial differential equations, linear equation system solvers, and tools for mean-variance portfolio optimization using quadratic programming. It also includes utilities for cleaning market data and tracking real-time volatility through noise-reduction filters.
The implementation is provided as a collection of interactive notebooks and code.
Features
- Quantitative Finance & Trading - Provides a comprehensive collection of numerical methods and models for quantitative finance and trading.
- Portfolio Optimization - Determines optimal asset allocations using quadratic programming and mean-variance optimization.
- Derivative Pricing Models - Provides mathematical models for computing option values, implied volatility, and risk metrics.
- Asset Allocation Optimization - Implements mathematical methods for determining optimal asset weights to balance risk and return.
- Asset Price Path Simulators - Implements stochastic processes like Geometric Brownian Motion to model future asset price movements.
- Option Pricing Models - Estimates the value of various option types using Monte Carlo simulations and binomial trees.
- Quadratic Programming Allocation - Provides mathematical optimization of portfolio weights using quadratic functions to manage variance and returns.
- Financial Parameter Estimation - Estimates time-varying volatility and autocorrelation using linear regression and filtering techniques.
- Calibration Frameworks - Matches model parameters to market data by fitting volatility smiles through root-finding methods.
- Numerical Inversion - Pricess options based on characteristic functions using fast Fourier transforms and numerical inversion.
- Differential Equation Solvers - Provides numerical solvers for partial differential equations to price options and jump-diffusion models.
- Linear System Solvers - Calculates matrix solutions using decomposition methods and iterative solvers for large equation sets.
- Volatility Calibration - Fits volatility smiles to market data using root-finding and filtering techniques.
