Forecasting Value at Risk with Deep Learning: Benchmarking LSTM Models Against Conventional Techniques

Sammanfattning

This project introduces new applications of machine learning in financial risk management. Two different deep learning models using Long Short-Term Memory (LSTM) are developed to estimate Value-at-Risk (VaR) at a 95% confidence level (α = 0.95). Using daily NASDAQ Composite Index (IXIC) data from 1993-01-01 to 2023-12-23, the LSTM models are evaluated against classical VaR models, e.g. Historical Simulations, and Normal Variance-Covariance, in both static (unconditional) and dynamic (conditional) volatility assumptions. The two LSTM models are built upon different frameworks and assumptions. The Quantile LSTM model uses direct quantile estimation to estimate VaR. The Parametric LSTM model forecasts the mean and standard deviation, and applies them to the Normal Variance-Covariance VaR equation. The LSTM models are successful in estimating VaR at a confidence level of α = 0.95. The violation rate for the Quantile LSTM is 5.17% and for the Parametric 5.43% close to the expected 5%, outperforming the classical models in both unconditional and conditional settings in violation rate accuracy. Both LSTM models pass the standard regulatory backtesting of VaR models: the Kupiec test, Christoffersen test, and the Conditional Coverage test. The models are retrained thirty times to evaluate the robustness of the model architecture due to stochasticity in the machine learning framework. Both model architectures displayed robustness in the retraining by continuously generating accurate VaR models in terms of stable violation rates close to 5%. Despite limitations, such as computational resources and a single asset focus with the NASDAQ index, the two LSTM based VaR models effectively capture nonlinear market dynamics and volatility clustering, offering a robust framework for VaR estimation in accordance with regulatory backtesting.