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.
This project addresses modeling and computational problems in financial risk management. Researchers and practitioners have developed powerful techniques for the design and valuation of complex derivative securities, but, as the recent financial crisis has shown, methods for measuring and managing risk have not kept up with the pace of innovation in new instruments. The goal of this project is to address this shortcoming through a combination of mathematical modeling, computational techniques, familiarity with industry practice, and understanding of the economic and regulatory environment. The project also seeks to train highly skilled individuals to work on these problems in industry, government, and universities. 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. (1) Risk measurement. In the wake of recent events, financial firms and regulators are rethinking simple approaches to risk taken in the past with a focus on longer horizons and more thorough exploration of scenarios and potential losses. This project's goals include development of new computational methods to address portfolio risk measurement, and (b) analysis of regulatory proposals for new risk charges that add dynamic features and computational complexity to more traditional static risk assessment. (2) Model calibration and model risk. Risk measurement relies on mathematical and computer models. Calibration is the iterative process of tuning a model to fit market data; model risk refers to potential errors in pricing and hedging that result from using a misspecified model. Model risk and model calibration are linked because fast methods for calibration allow the use of more complex and more realistic models, thus reducing model risk; fast calibration allows the use of multiple models for comparison; parameter instability in calibration provides a potential measure of model risk. A goal of this project is the development of methods for calibrating complex models that require computationally intensive procedures. (3) Default clustering and portfolio credit risk. Credit derivatives have featured prominently in the financial crisis, which has revealed the model risk in the industry's approach to pricing and hedging these securities. A goal of this project is to address the greatest shortcoming in the standard approach through a dynamic model that captures the critical effect of default clustering -- that is, the tendency for defaults to occur in clusters, rather than as purely isolated events. The project also addresses efficient computer simulation and calibration methods to facilitate the model's application. Numerous graduate students have participated in this project, completed their degress, and gone on to professional positions that build on their research training. In addition, the principal investigators have had extensive contacts and interactions with financial industry practitioners and financial regulators to enhance the impact of this research.