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Bayesian Modeling for Uncertainty Management in Financial Risk Forecasting and Compliance

Sharif Al Mamun, Rakib Hossain, Md. Jobayer Rahman, Malay Kumar Devnath, Farhana Afroz, Lisan Al Amin

TL;DR

The paper presents an end-to-end Bayesian framework for financial risk management that quantifies uncertainty across volatility forecasting, fraud detection, and compliance monitoring. It couples a Dynamic Linear Model for volatility, Bayesian logistic regression for fraud, and a hierarchical Beta state-space model for compliance, all supported by GPU-accelerated inference and Kafka-based ERP–FinTech integration. Out-of-sample results on S&P 500 volatility and VaR backtests show robust uncertainty quantification and competitive tail risk performance, while fraud detection achieves high AUC and interpretability, and compliance signals are transparent and adaptive. The work demonstrates practical deployment considerations and offers a path toward scalable, integrated risk governance in modern financial ecosystems.

Abstract

A Bayesian analytics framework that precisely quantifies uncertainty offers a significant advance for financial risk management. We develop an integrated approach that consistently enhances the handling of risk in market volatility forecasting, fraud detection, and compliance monitoring. Our probabilistic, interpretable models deliver reliable results: We evaluate the performance of one-day-ahead 95% Value-at-Risk (VaR) forecasts on daily S&P 500 returns, with a training period from 2000 to 2019 and an out-of-sample test period spanning 2020 to 2024. Formal tests of unconditional (Kupiec) and conditional (Christoffersen) coverage reveal that an LSTM baseline achieves near-nominal calibration. In contrast, a GARCH(1,1) model with Student-t innovations underestimates tail risk. Our proposed discount-factor DLM model produces a slightly liberal VaR estimate, with evidence of clustered violations. Bayesian logistic regression improves recall and AUC-ROC for fraud detection, and a hierarchical Beta state-space model provides transparent and adaptive compliance risk assessment. The pipeline is distinguished by precise uncertainty quantification, interpretability, and GPU-accelerated analysis, delivering up to 50x speedup. Remaining challenges include sparse fraud data and proxy compliance labels, but the framework enables actionable risk insights. Future expansion will extend feature sets, explore regime-switching priors, and enhance scalable inference.

Bayesian Modeling for Uncertainty Management in Financial Risk Forecasting and Compliance

TL;DR

The paper presents an end-to-end Bayesian framework for financial risk management that quantifies uncertainty across volatility forecasting, fraud detection, and compliance monitoring. It couples a Dynamic Linear Model for volatility, Bayesian logistic regression for fraud, and a hierarchical Beta state-space model for compliance, all supported by GPU-accelerated inference and Kafka-based ERP–FinTech integration. Out-of-sample results on S&P 500 volatility and VaR backtests show robust uncertainty quantification and competitive tail risk performance, while fraud detection achieves high AUC and interpretability, and compliance signals are transparent and adaptive. The work demonstrates practical deployment considerations and offers a path toward scalable, integrated risk governance in modern financial ecosystems.

Abstract

A Bayesian analytics framework that precisely quantifies uncertainty offers a significant advance for financial risk management. We develop an integrated approach that consistently enhances the handling of risk in market volatility forecasting, fraud detection, and compliance monitoring. Our probabilistic, interpretable models deliver reliable results: We evaluate the performance of one-day-ahead 95% Value-at-Risk (VaR) forecasts on daily S&P 500 returns, with a training period from 2000 to 2019 and an out-of-sample test period spanning 2020 to 2024. Formal tests of unconditional (Kupiec) and conditional (Christoffersen) coverage reveal that an LSTM baseline achieves near-nominal calibration. In contrast, a GARCH(1,1) model with Student-t innovations underestimates tail risk. Our proposed discount-factor DLM model produces a slightly liberal VaR estimate, with evidence of clustered violations. Bayesian logistic regression improves recall and AUC-ROC for fraud detection, and a hierarchical Beta state-space model provides transparent and adaptive compliance risk assessment. The pipeline is distinguished by precise uncertainty quantification, interpretability, and GPU-accelerated analysis, delivering up to 50x speedup. Remaining challenges include sparse fraud data and proxy compliance labels, but the framework enables actionable risk insights. Future expansion will extend feature sets, explore regime-switching priors, and enhance scalable inference.

Paper Structure

This paper contains 29 sections, 7 equations, 5 figures, 6 tables.

Table of Contents

  1. Introduction
  2. Literature Review
  3. Bayesian Methods in Financial Risk Management
  4. Time Series Forecasting with Dynamic Linear Models
  5. Fraud Detection Through Bayesian Networks
  6. Compliance Monitoring Applications
  7. Scalable Inference and Systems Integration
  8. Methodology
  9. Bayesian update and decision layer
  10. Data Acquisition & Preprocessing
  11. Bayesian Model Frameworks
  12. Dynamic Linear Model (DLM) for Volatility Forecasting
  13. Bayesian Logistic Regression for Fraud Detection
  14. Hierarchical Beta Compliance Model
  15. Computational Optimizations
  16. ...and 14 more sections

Figures (5)

  • Figure 1: Research Workflow Diagram
  • Figure 2: Conceptual ERP-to-FinTech streaming architecture using Apache Kafka. The proposed framework enables low-latency (< 2 s) data ingestion and normalization between enterprise ERP systems (e.g., SAP, Oracle) and Bayesian FinTech microservices. It supports real-time probabilistic risk analytics through GPU-accelerated inference and secure 5G RedCap edge connectivity.
  • Figure 3: One-step-ahead forecasts of log-realized volatility versus actual values for the S&P 500 index. Negative values correspond to the logarithm of realized volatility $\bigl(y_t = \log(\mathrm{RV}_t)\bigr)$, not to raw volatility magnitudes.
  • Figure 4: ROC Curve for Fraud Detection
  • Figure 5: Trajectories of Compliance Risk Parameters