Computational Methods in Risk Management and Financial Engineering

Columbia University, New York NY

Investigators

Abstract

This project addresses modeling and computational problems in financial risk management. Meeting current challenges in risk management requires combining mathematical modeling and computational techniques with an understanding of industry practice and the economic and regulatory environment. This project focuses on three topics from this perspective: (1) large-scale portfolio risk measurement; (2) model calibration and model risk; (3) default clustering and portfolio credit risk. Across these topics, the investigators will develop mathematical models of risk and computational methods for the efficient calculation of risk. Specific objectives include the development of efficient Monte Carlo methods for portfolio risk measurement, model calibration, and evaluating portfolio credit risk in the presence of default clustering. In the wake of the current crisis, financial firms and regulators are rethinking simple approaches to risk taken in the past with a new focus on longer horizons and more thorough exploration of scenarios and potential losses. This project will address mathematical modeling and computational problems that arise in the development of new approaches to risk measurement. Computational complexity is often a major constraint in realistic assessment of risk; advances in computing methods need to be closely tied to the development of new models to be effective. More broadly, the field of quantitative finance is in transition, with the highest near-term priorities for research and education shifting away from structured derivative securities to risk management. The investigators are active in this transition through their research, teaching, interactions with practitioners and regulators, and participation in educational standard setting through professional risk management organizations. This project aligns with their activities across these areas, including mentoring students and developing and updating courses at all levels. The U.S.'s leadership in the intensely competitive global financial services industry has relied on a large influx of highly trained talent from the mathematical sciences. This project will help maintain this base of talent and help shift academic research and training to the highest near-term priorities and to emerging areas of quantitative finance with the greatest growth potential.