Carbon Option Pricing under a Stochastic Volatility Framework
As the world transitions toward a low-carbon economy, carbon markets have emerged as
critical tools in the fight against climate change. A carbon credit represents the right to emit—
or offset—one ton of carbon dioxide or its equivalent in greenhouse gases. These credits are
generated through initiatives such as renewable energy development, reforestation, and
carbon capture technologies, and are actively traded on global markets.
According to Carbon Market Watch, Shell was the largest purchaser in the voluntary carbon
market in 2024, retiring approximately 14.9 million carbon credits, with more than half used in
December alone. This was nearly three times the volume of Microsoft, the second-largest
buyer. Other major buyers in the oil and gas sector included Eni (6 million credits), Engie (2.1
million), Woodside Energy (1.4 million), and PetroChina (1.2 million), each using carbon credits
as part of their broader climate strategies. These real-world practices highlight the increasing
reliance on carbon credits, while raising important questions about their credibility,
transparency, and environmental effectiveness.
This iRisk Lab project investigates financial modeling techniques to better understand and
manage carbon-related assets. Specifically, we develop a pricing framework for carbon options,
where the underlying asset is a carbon futures contract based on carbon credits, modeled
under a stochastic volatility process. Our approach is grounded in the methodology proposed
by Zhe Liu and Yanbin Li (2025), Carbon Option Pricing and Carbon Management under
Uncertain Finance Theory, published in Communications in Statistics – Theory and Methods. If
time permits, we analyze the carbon credit asset market further.
Supervisor: Tolulope Fadina
Graduate Supervisor: Yasintorn Wongwoottisaroch
Climate Data Discovery and Consolidation
As data-driven decision-making becomes increasingly vital in addressing climate-related
challenges, it is crucial to build a comprehensive understanding of climate datasets that support
research and innovation in climate risk assessment and mitigation. This project aims to conduct
an extensive climate data discovery process within UIUC, focusing on identifying and cataloging
datasets across units, research centers, and government entities, with a special emphasis on
climate risk, insurance, and actuarial applications. By consolidating these diverse climate-
related datasets into a centralized repository, we aim to create a unified platform that
empowers researchers, students, and faculty members to analyze and model climate risks more
effectively.
The project aligns with SOA’s objectives by supporting the development of data-driven tools
and methodologies for assessing risks associated with extreme weather events. The repository
will include datasets relevant to climate science, risk modeling, financial exposure, and loss
estimation, bridging the gap between meteorological data and actuarial applications. We
anticipate that this initiative will involve dedicated personnel for climate data integration,
interactive visualization, and the development of a relational database that facilitates
interdisciplinary research in climate risk, resilience, and insurance modeling.
Supervisor: Zhiyu (Frank) Quan
Graduate Supervisor: Jiayi Guo
Decentralized Trading and Risk in the Crypto Market
The rapid growth of blockchain technology and the expanding cryptocurrency market have
created exciting new opportunities as well as challenges. While the novel, decentralized trading
mechanisms of crypto markets offer unique benefits — such as greater accessibility,
transparency, and efficiency — they can also attract malicious actors seeking to exploit
vulnerabilities.
In this project, we will take a closer look at how trading works in both centralized exchanges
(CEX) and decentralized exchanges (DEX):
- CEX platforms, like Binance or Coinbase, operate much like traditional stock markets.
Buyers and sellers post bids and asks, and a central operator (or market maker) matches
these orders. Market makers actively adjust their quotes to manage inventory, respond
to market news, and provide liquidity when they see opportunities to profit from price
movements. - DEX platforms, like Uniswap or Sushiswap, work differently. They use automated market
maker (AMM) protocols that enable trading without a central authority. Prices are set
dynamically by smart contracts using liquidity pools, which anyone can contribute to. A
distinctive feature of DEXs is the requirement for blockchain gas fees, which can vary
depending on network congestion and transaction urgency.
Throughout the semester, we will explore the unique features of decentralized exchanges, gain
deeper insight into how these innovative markets operate, investigate their advantages and
potential vulnerabilities, and put our hypotheses to the test using real blockchain data.
Supervisor: Xiaochen Jing
Graduate Supervisor: Zhonghe Wan
Model Governance and Ethics for GenAI Models
Transformer-based Large Language Models (LLMs) have significantly accelerated the development of AI-assisted applications in real-world settings. In the business operation, balancing the need for robust, data-driven AI models with the ethical imperatives of fairness and privacy is a complex, yet essential, task.
In response to these challenges, there is a growing recognition that Generative AI (GenAI) models must be designed with a broader set of criteria in mind. There is also growing attention in the research community toward aligning AI models with real-world societal needs and values. Although various solutions have been proposed to address these concerns, there remains limited research on their effectiveness within the insurance sector. This project aims to bridge the gap between emerging AI fairness evaluation methods, debiasing techniques, and model interpretability, proposed in computer science or statistics communities—and the current lack of structured ethical and governance frameworks for practical AI implementation in the insurance sector. We try to identify AI solutions that are appropriate for the insurance sector and translate them into actuarial terms to facilitate easier understanding and adoption within the profession.
This project aims to address the following key areas and develop practical guidelines to support actuarial practices in the ethical and responsible use of GenAI systems within the insurance sector: (1) Deploying and Operationalizing GenAI for Insurance Use Cases; (2) Ensuring Reliability and Governance in GenAI; (3) Fair and Ethical GenAI; (4) GenAI Compliance with Insurance Regulatory.
Supervisor: Zhiyu (Frank) Quan
Graduate Supervisor: Panyi Dong
Introduction to Monte Carlo Simulation
Monte Carlo simulation is a technique for predicting outcomes involving uncertain events.
Analysts can use these methods to quantify risks with statistics like value at risk and tail value at
risk. In addition, actuaries can estimate the likelihood of certain events, such as the probability
of ruin or the probability of turning a profit.
In this educational project, students will learn to design Monte Carlo simulations, evaluate their
strengths and limitations, and apply them to real-world actuarial problems.
- Introduction to Monte Carlo Methods
- Study examples of Monte Carlo simulations, such as
- Estimating constants like e and
- Monte Carlo integration
- Random Walks
- Review important mathematical and actuarial models, including
- (Geometric) Brownian Motion
- Aggregate Loss Distributions
- Binomial Option Pricing
- Study examples of Monte Carlo simulations, such as
- Model Building and Simulation Experiments
- Build simulations in Python and upload them to GitHub.
- Apply sensitivity analysis by altering assumptions.
- Gauge model risk
- Compare simulation statistics to analytic results when possible.
- Investigate regulatory reserve requirements.
- Basel Accords
- Solvency II
- Results Interpretation and Reporting
- Summarize findings and evaluate the efficacy of the simulations.
- Discuss implications for actuarial risk management.
- Present findings at the end of the semester to other IRisk groups.
This project does not aim to produce published research; instead, it will give a hands-on, practical introduction to Monte Carlo simulation methods. We will have weekly in-person team meetings at my office, 272 CAB, to discuss progress. There will also be individual meetings as needed to discuss members’ contributions. Students must commit at least five hours a week to the project, including meetings.
Supervisor: Eric Icaza
PCMI Warranty Data Innovation Project
Overview
This project engages students from the University of Illinois in a practical, hands-on experience with PCMI, a leader in software solutions for warranties. The project aims to explore new data product opportunities, develop a business case, and support the design and development of innovative data-driven products.
Goals
- Identify New Data Product Opportunities: Students will investigate three potential areas for data product innovation:
- Enhancing existing products by integrating analytics directly into them.
- Developing new standalone data products for current customers.
- Creating new standalone data products targeted at new market segments.
- Develop a Business Case: Each team will establish a business case to justify the investment in their proposed data products. This includes market analysis, potential ROI, and strategic alignment with PCMI’s objectives.
- P&L Model Development: Over the course of the project, students will build a profit and loss (P&L) model for the proposed data products, detailing anticipated revenue, cost, and margin scenarios.
- Identify Data Augmentation Partners: Teams will research and propose potential partners for data augmentation to enhance the value of PCMI’s data products.
- Requirements and Solution Design: Students will develop detailed requirements for the approved new data products and collaborate with the PCMI RDR (Research, Development, and Requirements) team on the solution design.
- Development Backlog Creation: Following Minimum Viable Product (MVP) best practices, students will create a development backlog for a PCMI development team to execute.
Expected Outcomes
- A portfolio of new data product ideas fully explored and documented.
- Comprehensive business cases supporting further investment in new products.
- A robust P&L model for each proposed product.
Deliverables
- Final report detailing research findings, business cases, P&L models, and product requirements.
- Presentation to PCMI stakeholders showcasing proposed data products and strategic insights.
- Development backlog ready for implementation by PCMI’s development team.
Evaluation
- Quality and innovation of data product ideas.
- Feasibility and thoroughness of the business cases.
- Practicality and detail in the P&L models and development plans.
- Engagement with potential data augmentation partners and early adopters.
This project proposal offers a unique opportunity for students to apply their academic knowledge to real-world challenges, fostering innovation and strategic thinking in the development of new data products at PCMI.
Supervisors: Zhiyu Quan, PCMI Project Manager
Graduate Supervisor: Yiwei Wang
RGA Financial Models
This R&D project explores the development and assessment of various data-driven financial cash models to manage RGA’s global financial service products including longevity swaps, asset-intensive transactions, and pension risk transfers. Transaction-specific data runs the spectrum from voluminous to sparse. Transactions typically range from $100 million to $10+ billion. Participants will apply actuarial science and data science to develop various proxy models and assess underlying assumptions. Models are used to monitor performance, risk profiles, manage capital, and provide insights into business management.
The IRisk team will collaborate with RGA Global Financial Services (GFS) Valuation Team Europe-Middle-East-Africa (EMEA) actuaries led by former ARMS instructor, Tim Cardinal. Fall 2025 will focus on learning the business, models, and data, developing problem definitions, and building prototypes. Fall 2025 will focus on operationalizing prototypes and learning insights into models’ strengths and weaknesses as they are applied to recent/new transactions. Without going into details, the work will be engaging, challenging, and exciting.
Students will be required to sign a non-disclosure agreement (NDA). In your application, please indicate your interest in internships and co-ops. Ideally, we would like 1-3 of the IRisk student team to intern during summer 2026 and 1-2 students to co-op in fall and/or spring 2026.
RGA is one of the largest global life and health reinsurers and is #223 on the Fortune 500 with offices in dozens of countries around the world from St. Louis and Toronto to London, Dublin, Paris, and Milan to Hong Kong, Shanghai, Beijing, Tokyo, Mubai, and Dubai.
Supervisors: Xiaochen Jing, Frank Quan, Tim Cardinal, RGA GFS Valuation EMEA team