Welcome to the AFMA Quant-AI Lab, a quantitative research repository dedicated to bridging the gap between classical financial econometrics and modern continuous-time Deep Learning.
"Complexity must earn its place."
In quantitative finance, machine learning models frequently overfit to noise and fail catastrophically out-of-sample. This lab operates on a strict scientific principle: No AI model is accepted unless it can mathematically and empirically defeat a highly optimized, domain-specific classical baseline. Every neural architecture built here is stress-tested against structural market breaks, exogenous shocks, and volatility clustering.
Focus: Physics-Informed Neural Networks (PINNs) for Single-Quantile Risk Forecasting.
- Explored the transition from historical simulation to deep learning for predicting the 95% and 99% Value at Risk (VaR).
- Key takeaway: Predicting a single quantile leaves the portfolio blind to the shape of the tail. This limitation motivated the transition to Project 02.
Focus: Continuous-Time Neural SDEs, Path Signatures, and Full Probability Distributions.
- Moving beyond point estimates to forecast the entire probability distribution of tomorrow's returns.
- Classical Baselines Built: GARCH(1,1), MLE-fitted Student-t, and a proprietary factor-normalized VIX-Scaled Student-t model.
- AI Architecture: Implementing Rough Path Theory (Signatures) and Neural Stochastic Differential Equations (SDEs) to capture non-linear, idiosyncratic market microstructure.
- Mathematics: Stochastic Calculus, Rough Path Theory, Maximum Likelihood Estimation (MLE), Kolmogorov-Smirnov Tests.
- Machine Learning: Neural SDEs, Deep Signature Transforms, Physics-Informed Regularization.
- Engineering: Python, PyTorch, SciPy (Nelder-Mead optimization), Pandas/NumPy (vectorized backtesting).
Developed as part of the AFMA Quant-AI Lab research series.