20250528 無限數學科學研究社

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12:10 - 12:20 黃馨霈 

Evaluating Tail Risk in Bitcoin Using Stochastic Volatility and Correlated Jump Models under Basel Standards

This thesis investigates the measurement of tail risk in cryptocurrency markets through the lens of Value-at-Risk (VaR) and Expected Shortfall (ES), with a focus on regulatory relevance under the Basel III framework. Using daily Bitcoin data from 2018 to 2024, we assess the performance of four models widely used in financial risk modeling: Black-Scholes (BS), Stochastic Volatility (SV), Stochastic Volatility with Jumps (SVJ), and Stochastic Volatility with Correlated Jumps (SVCJ). Each model is used to generate one-step-ahead forecasts of VaR and ES over rolling windows, and evaluated across multiple holding periods (1, 14, and 28 days) and confidence levels (95\% and 99\%). Backtesting results based on the Traffic Light approach, Kupiec’s Proportion of Failures (POF) test, Christoffersen’s Conditional Coverage (CC) test, and the Acerbi–Szekely ($Z_1$–$Z_3$) tests for ES reveal that the SVCJ model consistently achieves superior accuracy in capturing extreme losses, particularly for longer horizons. The results suggest that incorporating both volatility clustering and jump dependence, as captured by the SVCJ model, significantly improves the precision and prudence of tail risk estimation for digital assets. This highlights the importance of selecting appropriate models in the context of cryptocurrency risk assessment and carries practical implications for financial institutions and regulators seeking to incorporate crypto-assets into capital adequacy evaluations and stress testing procedures.

12:20- 12:30 施昱全 

Qualitative Insights Meet Quantitative Forecasts with GPT-4o Mini for Taiwan Earnings Prediction

This study explores the potential of large language models (LLMs), particularly GPT-4o Mini, to enhance earnings forecasting by transforming structured financial data into qualitative textual analysis. Using income statements, balance sheets and Statements of cash flows from Taiwan-listed firms, GPT-4o Mini generates descriptive reports through carefully designed prompts, including Chain-of-Thought (CoT) reasoning. These textual outputs are converted into numerical embeddings, which are subsequently used in prediction models. We benchmark GPT-4o Mini’s forecasts against traditional classifiers such as Logistic Regression and XGBoost. Results reveal that while GPT-4o Mini alone does not outperform established methods, CoT prompting significantly improves its predictive performance and interpretability. This study highlights the complementary role LLMs can play in financial analysis, bridging qualitative narrative understanding and quantitative forecasting.

12:30 - 12:40 吳柏賢 

Redesigning Solar Contracts to Unlock Long-Term ESG Investment

This thesis addresses financing challenges in Taiwan’s green energy sector, with a focus on Environmental, Social, and Governance (ESG) objectives. Using case studies of Chailease Holding and the Citizen Power Plant, we explore asset securitization as a strategy to overcome funding constraints in solar energy projects. A critical gap in current 20-year power purchase agreements (PPAs) is their failure to account for long-term project value and post-contract electricity price risk, which undermines investor confidence and fundraising. We propose two redesigned contracts to mitigate these issues. Solution 1 offers a post-PPA price guarantee: investors exchange a portion of future revenue for a minimum electricity price from Chailease Co., reducing long-term price uncertainty and aligning incentives by making Chailease a partial residual claimant. Solution 2 introduces interval protection, where investors receive price support within a defined range after the PPA ends, limiting both downside risk and over-guarantee distortions. We further address model risk in pricing these contracts. Specifically, we compare the standard Black-Scholes model with a more realistic electricity price process that incorporates stochastic volatility and correlated jumps. Sensitivity analysis highlights how model choice affects contract valuation and risk exposure. Together, these solutions enhance financial stability, improve incentive alignment, and support ESG-aligned renewable energy development. The proposed framework offers a practical and replicable approach for designing long-term financing mechanisms in emerging markets facing similar investment risks.

12:40 - 12:50 陳怡仁

Bridging Interpretability and Performance: Augmented Features and PowerSHAP for Credit Default Prediction

As AI models become more complex, improving their interpretability without losing accuracy is a major concern, especially in regulated areas like credit scoring. Although models like XGBoost offer strong predictive performance, their black-box nature does not meet transparency standards required by financial regulations. This paper tackles this issue using two public credit default datasets from Kaggle. We create a unified data preprocessing pipeline and an interpretable, performance-focused modeling approach. Key features are selected using PowerSHAP on the XGBoost model (Verhaeghe et al., 2022), and then enhanced with polynomial and interaction terms to build an expanded feature set. We show that logistic regression, when used with this enriched data, significantly improves AUC while keeping the model interpretable. In comparison, XGBoost sees only a slight AUC gain with the same features, showing that added complexity brings limited benefits for already strong models. Our results offer a practical and efficient way to balance accuracy and interpretability in AI-based credit scoring.

12:50 - 13:00 陳諾恆

Mapping Risk Contagion through Graphical Models and Early Warning Signals in Taiwan’s Stock Market

This paper leverages graphical models to investigate systemic risk in Taiwan’s financial markets, focusing on the dynamic interactions among the 30 largest market-capitalization firms from January 1985 to April 2025. We compare two approaches: the Granger causality network, which captures directional predictability among firms’ returns, and the Functional Structural Equation Model (FSEM), a technique recently adapted from neuroscience to estimate causal relations in high-dimensional functional data \citep{billio2012econometric,lee2022functional}. Our analysis highlights significant shifts in network centrality over time, with financial and telecommunications sectors emerging as key influencers—contrary to the commonly held belief in the dominance of technology firms. By measuring network connectivity through degree centrality, closeness, and eigenvector centrality, we propose an early warning mechanism for identifying periods of heightened systemic risk. The results offer practical implications for institutional risk management and individual investment strategies, demonstrating the value of network-based models in financial risk monitoring.