Risk Modeling

Deep Generative Models for Synthetic Financial Data: Applications to Portfolio and Risk Modeling ArXiv ID: 2512.21798 “View on arXiv” Authors: Christophe D. Hounwanou, Yae Ulrich Gaba Abstract Synthetic financial data provides a practical solution to the privacy, accessibility, and reproducibility challenges that often constrain empirical research in quantitative finance. This paper investigates the use of deep generative models, specifically Time-series Generative Adversarial Networks (TimeGAN) and Variational Autoencoders (VAEs) to generate realistic synthetic financial return series for portfolio construction and risk modeling applications. Using historical daily returns from the S and P 500 as a benchmark, we generate synthetic datasets under comparable market conditions and evaluate them using statistical similarity metrics, temporal structure tests, and downstream financial tasks. The study shows that TimeGAN produces synthetic data with distributional shapes, volatility patterns, and autocorrelation behaviour that are close to those observed in real returns. When applied to mean–variance portfolio optimization, the resulting synthetic datasets lead to portfolio weights, Sharpe ratios, and risk levels that remain close to those obtained from real data. The VAE provides more stable training but tends to smooth extreme market movements, which affects risk estimation. Finally, the analysis supports the use of synthetic datasets as substitutes for real financial data in portfolio analysis and risk simulation, particularly when models are able to capture temporal dynamics. Synthetic data therefore provides a privacy-preserving, cost-effective, and reproducible tool for financial experimentation and model development. ...

Synthetic Financial Data Generation for Enhanced Financial Modelling ArXiv ID: 2512.21791 “View on arXiv” Authors: Christophe D. Hounwanou, Yae Ulrich Gaba, Pierre Ntakirutimana Abstract Data scarcity and confidentiality in finance often impede model development and robust testing. This paper presents a unified multi-criteria evaluation framework for synthetic financial data and applies it to three representative generative paradigms: the statistical ARIMA-GARCH baseline, Variational Autoencoders (VAEs), and Time-series Generative Adversarial Networks (TimeGAN). Using historical S and P 500 daily data, we evaluate fidelity (Maximum Mean Discrepancy, MMD), temporal structure (autocorrelation and volatility clustering), and practical utility in downstream tasks, specifically mean-variance portfolio optimization and volatility forecasting. Empirical results indicate that ARIMA-GARCH captures linear trends and conditional volatility but fails to reproduce nonlinear dynamics; VAEs produce smooth trajectories that underestimate extreme events; and TimeGAN achieves the best trade-off between realism and temporal coherence (e.g., TimeGAN attained the lowest MMD: 1.84e-3, average over 5 seeds). Finally, we articulate practical guidelines for selecting generative models according to application needs and computational constraints. Our unified evaluation protocol and reproducible codebase aim to standardize benchmarking in synthetic financial data research. ...

Comparative Evaluation of VaR Models: Historical Simulation, GARCH-Based Monte Carlo, and Filtered Historical Simulation ArXiv ID: 2505.05646 “View on arXiv” Authors: Xin Tian Abstract This report presents a comprehensive evaluation of three Value-at-Risk (VaR) modeling approaches: Historical Simulation (HS), GARCH with Normal approximation (GARCH-N), and GARCH with Filtered Historical Simulation (FHS), using both in-sample and multi-day forecasting frameworks. We compute daily 5 percent VaR estimates using each method and assess their accuracy via empirical breach frequencies and visual breach indicators. Our findings reveal severe miscalibration in the HS and GARCH-N models, with empirical breach rates far exceeding theoretical levels. In contrast, the FHS method consistently aligns with theoretical expectations and exhibits desirable statistical and visual behavior. We further simulate 5-day cumulative returns under both GARCH-N and GARCH-FHS frameworks to compute multi-period VaR and Expected Shortfall. Results show that GARCH-N underestimates tail risk due to its reliance on the Gaussian assumption, whereas GARCH-FHS provides more robust and conservative tail estimates. Overall, the study demonstrates that the GARCH-FHS model offers superior performance in capturing fat-tailed risks and provides more reliable short-term risk forecasts. ...

Generalization of the Alpha-Stable Distribution with the Degree of Freedom ArXiv ID: 2405.04693 “View on arXiv” Authors: Unknown Abstract A Wright function based framework is proposed to combine and extend several distribution families. The $α$-stable distribution is generalized by adding the degree of freedom parameter. The PDF of this two-sided super distribution family subsumes those of the original $α$-stable, Student’s t distributions, as well as the exponential power distribution and the modified Bessel function of the second kind. Its CDF leads to a fractional extension of the Gauss hypergeometric function. The degree of freedom makes possible for valid variance, skewness, and kurtosis, just like Student’s t. The original $α$-stable distribution is viewed as having one degree of freedom, that explains why it lacks most of the moments. A skew-Gaussian kernel is derived from the characteristic function of the $α$-stable law, which maximally preserves the law in the new framework. To facilitate such framework, the stable count distribution is generalized as the fractional extension of the generalized gamma distribution. It provides rich subordination capabilities, one of which is the fractional $χ$ distribution that supplies the needed ‘degree of freedom’ parameter. Hence, the “new” $α$-stable distribution is a “ratio distribution” of the skew-Gaussian kernel and the fractional $χ$ distribution. Mathematically, it is a new form of higher transcendental function under the Wright function family. Last, the new univariate symmetric distribution is extended to the multivariate elliptical distribution successfully. ...

Equity Risk Premiums (ERP): Determinants, Estimation and Implications - A Post-Crisis Update ArXiv ID: ssrn-1492717 “View on arXiv” Authors: Unknown Abstract Equity risk premiums are a central component of every risk and return model in finance and are a key input into estimating costs of equity and capital in both c Keywords: equity risk premium, cost of equity, capital asset pricing model, valuation, risk modeling, Equities Complexity vs Empirical Score Math Complexity: 4.0/10 Empirical Rigor: 3.0/10 Quadrant: Philosophers Why: The paper is conceptually oriented, discussing determinants and estimation methods for equity risk premiums without presenting advanced mathematical derivations or rigorous empirical backtesting with specific datasets and performance metrics. flowchart TD A["Research Goal<br>Determine Post-Crisis ERP"] --> B["Methodology<br>Historical & Cross-Sectional Analysis"] B --> C{"Key Inputs<br>Data Sources"} C --> C1["US Equity Returns"] C --> C2["Risk-Free Rates<br>T-Bills/Bonds"] C --> C3["Inflation & Macro Indicators"] C --> D["Computational Processes"] D --> D1["Implied ERP Calculation"] D --> D2["Historical ERP Estimation"] D --> D3["Risk Model Integration<br>CAPE/Dividend Models"] D1 & D2 & D3 --> E["Key Findings<br>Outcomes"] E --> E1["ERP ≈ 4.5-5.5%<br>Post-Crisis Estimate"] E --> E2["ERP is Non-Constant<br>Varies with Market Conditions"] E --> E3["Cost of Equity<br>ERP + Risk-Free Rate"] E --> E4["Valuation Implications<br>Lower Discount Rates"]