Abstract
The integration of computational intelligence and machine learning provides a robust paradigm for navigating complex, real-world challenges like extreme market volatility. While executive management relies on a single, decisive metric: Value at Risk and Expected Shortfall to dictate risk exposure, traditional Gaussian models frequently miscalculate these boundaries. To resolve this, we propose a Deep Parametric Risk Architecture. We systematically extend Value at Risk and Expected Shortfall computation into non-Gaussian environments by integrating a Long Short-Term Memory network with four distinct heavy-tailed mathematical engines: Student's t, Cauchy, Rayleigh, and Lévy distributions. Utilizing dynamic temporal feature extraction, the neural network continuously calibrates distribution parameters to capture non-linear volatility clustering. Comprehensive backtesting demonstrates that static Gaussian baselines systematically underestimate risk, resulting in severe limit breaches. Conversely, unconstrained heavy-tailed models mathematically eliminate violations but induce excessive capital requirements. The constrained Long Short-Term Memory network with Student's t architecture achieves an optimal regulatory balance, yielding a precise violation rate of 0.39% and satisfying the Kupiec Proportion of Failures test (p-value = 0.1087). Ultimately, to satisfy strict regulatory reporting mandates against pure black-box models, this research fuses deep learning with statistical mechanics into a hybrid system, advancing computational intelligence in robust institutional risk management.