Fast Simulation Methods for Risk Management

Columbia University, New York NY

Investigators

Abstract

Computer simulation is widely used in measuring and managing risk. The objective of this project is to develop fast simulation methods for risk management, focusing on three specific problems: (1) estimation of value-at-risk and related measures of the risks resulting from changes in market prices; (2) estimation of portfolio credit risk; and (3) estimation of ruin probabilities and insurance risk. Each of these problems poses a computational challenge at least in part because it involves aspects of rare event simulation. This project seeks to develop variance reduction techniques, based primarily on importance sampling, specifically designed to address the key sources of difficulty in each case. From a methodological perspective, the research challenge lies primarily in two issues: (a) these applications often require developing methods suitable for heavy-tailed distributions to which traditional rare event simulation methods are inapplicable; (b) the models used in these applications often involve complex dependence between sources of risk, and this too complicates the development of variance reduction techniques. Both issues are of central importance in practice because risk management is necessarily concerned with tail events and with the extent to which spreading risk reduces risk. Sound risk management is essential to the stability of the nation's financial system. Yet firms sometimes view it as a cost of complying with regulations rather than as a source of competitive advantage and therefore underinvest in developing the necessary tools. Funded academic research has an important role to play in advancing risk management methods. The US is currently a world leader in developing quantitative methods for the financial services industry. Its success relies primarily on its educational base and supply of highly trained individuals. With its proximity to one of the world's major financial centers, Columbia University is particularly well positioned to be a leader in research and education in this area. This project is part of a network of research and educational activities at Columbia. In addition to supporting the PIs' research it will support doctoral students and foster research interactions with industry.