FinML: Financial Machine Learning Library

A comprehensive library for applying machine learning techniques to financial markets, specializing in options pricing, volatility modeling, and arbitrage detection.

Overview

FinML implements state-of-the-art machine learning models tailored for financial applications, with a focus on:

• Volatility surface modeling and forecasting
• Arbitrage detection in options markets
• Neural network-based trading strategies
• Time series prediction for financial data

Key Features

Volatility Surface Arbitrage Detection

The library provides tools to:

• Build and visualize complete implied volatility surfaces
• Detect calendar spread and butterfly arbitrage opportunities
• Predict future volatility surfaces using CNN-LSTM hybrid models
• Calculate no-arbitrage bounds for implied volatility

Neural Network Architectures

• LSTM: For time series prediction of financial data
• CNN: For pattern recognition
• Hybrid Models: Combining convolutional layers for spatial features with LSTM layers for temporal dynamics

Options Pricing

• Black-Scholes model implementation
• Implied volatility calculation
• Greeks estimation
• Monte Carlo simulation for pricing complex derivatives

Getting Started

Prerequisites

• C++17 compatible compiler
• CMake 3.10 or higher
• Python 3.8+ (for visualization scripts)
• Required Python packages: pandas, numpy, matplotlib, seaborn

Building the Library

mkdir build && cd build
cmake ..
make

Running the Demos

Several demo applications are provided to showcase the library's capabilities:

1. Volatility Surface Arbitrage Detection:

./bin/volatility_surface_arbitrage

2. LSTM Options Arbitrage:

./bin/lstm_options_arbitrage

3. Hybrid Trading Model:

./bin/run_hybrid_trading_model

Visualizing Results

The library outputs results to CSV files that can be visualized using the provided Python scripts:

python ../python/visualize_vol_surface.py
python ../python/analyze_arbitrage.py

These scripts generate comprehensive visualizations including:

• 3D volatility surfaces
• Arbitrage opportunity heatmaps
• Volatility smile plots
• Prediction error analysis
• No-arbitrage bound comparisons

Volatility Surface Arbitrage Detection

The volatility surface arbitrage detection module implements two primary types of arbitrage detection:

Calendar Spread Arbitrage

Calendar spread arbitrage occurs when the implied volatility for a longer-term option is lower than that of a shorter-term option with the same strike price. This violates the principle that implied volatility should generally increase with time to maturity.

The detector checks for:

• Decreasing volatility across increasing maturities
• Quantifies the magnitude of the arbitrage opportunity
• Provides detailed descriptions of each identified opportunity

Butterfly Arbitrage

Butterfly arbitrage occurs when the volatility smile exhibits a non-convex shape across strike prices. This violates the principle that the implied volatility curve should be convex.

The detector:

• Checks for violations of convexity in the volatility smile
• Quantifies the arbitrage magnitude using weighted averages
• Identifies the specific strikes and maturities where arbitrage exists

CNN-LSTM Hybrid Architecture

The volatility surface prediction model uses a hybrid architecture that combines:

1. Convolutional layers to capture the spatial structure of the volatility surface across strikes and maturities
2. LSTM layers to model the temporal evolution of these surfaces
3. Self-attention mechanisms to weight the importance of different regions of the surface

This approach enables the model to:

• Learn the typical shapes of volatility smiles and term structures
• Understand how these structures evolve over time
• Identify potential arbitrage opportunities before they become apparent in the market

License

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

Acknowledgments

• The SSVI (Surface Stochastic Volatility Inspired) model by Gatheral and Jacquier
• Research on no-arbitrage conditions for volatility surfaces
• The deep learning community for advances in time series forecasting techniques