Analytics

In this research, we summarize the results of implementing the market risk premium into the option valuation formulas of the Black–Scholes–Merton model for out-of-the-money (OTM) options. We show that derivative prices can partly depend on systematic market risk, which the BSM model ignores by construction. Specifically, empirical studies are conducted using 50ETF options obtained from the Shanghai Stock Exchange, covering the periods from January 2018 to September 2022 and from December 2023 to October 2025. The pricing of the OTM options shows that the adjusted BSM formulas exhibit better pricing performance compared with the market prices of the OTM options tested. Furthermore, a framework for the empirical analysis of option prices based on the Capital Asset Pricing Model (CAPM) or factor models is discussed, which may lead to option formulas using non-homogeneous heat equations. The later proposal requires further statistical testing using real market data but offers an alternative to the existing risk-neutral valuation of options.

The COVID-19 pandemic disrupted traditional patterns of sport consumption, raising questions about whether fans would return to stadiums and how sensitive they would be to ticket prices in the recovery period. This study reconceptualizes ticket price elasticity as a market-based indicator of fan loyalty and applies it to Major League Baseball (MLB) during 2021–2023. Using team–season attendance data from Baseball-Reference, primary-market ticket prices from the Team Marketing Report Fan Cost Index, and secondary-market prices from TicketIQ, we estimate log–log fixed-effects panel models to separate causal price responses from popularity-driven correlations. The results show a strongly negative elasticity of attendance with respect to primary-market prices (β ≈ −7.93, p < 0.001), indicating that higher ticket prices substantially reduce attendance, while secondary-market prices are positively associated with attendance, reflecting demand shocks rather than causal effects. Heterogeneity analyses reveal that brand strength, team performance, and game salience significantly moderate elasticity, supporting the interpretation of inelastic demand as revealed loyalty. These findings highlight the potential of elasticity as a Fan Loyalty Index, providing a replicable framework for measuring consumer resilience. The study offers practical insights for pricing strategy, fan segmentation, and engagement, while emphasizing the broader social role of sport in restoring community identity during post-pandemic recovery.

This study presents the development of an AI-powered chatbot designed to facilitate accurate and efficient retrieval of information from the FDA drug labeling documents. Leveraging OpenAI’s GPT-3.5-turbo model within a controlled, document-grounded question–answering framework, Chatbot was created, which can provide users with answers that are strictly limited to the content of the uploaded drug label, thereby minimizing hallucinations and enhancing traceability. A user-friendly interface built with Streamlit allows users to upload FDA labeling PDFs and pose natural language queries. The chatbot extracts relevant sections using PyMuPDF and regex-based segmentation and generates responses constrained to those sections. To evaluate performance, semantic similarity scores were computed between generated answers and ground truth text using Sentence Transformers. Results across 10 breast cancer drug labels demonstrate high semantic alignment, with most scores ranging from 0.7 to 0.9, indicating reliable summarization and contextual fidelity. The chatbot achieved high semantic similarity scores (≥0.95 for concise sections) and ROUGE scores, confirming strong semantic and textual alignment. Comparative analysis with GPT-5-chat and NotebookLM demonstrated that our approach maintains accuracy and section-specific fidelity across models. The current work is limited to a small dataset, focused on breast cancer drugs. Future work will expand to diverse therapeutic areas and incorporate BERTScore and expert-based validation.