Review of risk management: value at risk and beyond, edited by M.A.H. Dempster. Cambridge University Press 2002.

This book is a collection of nine papers presented at a Workshop on Risk Management held at the Isaac Newton Institute for Mathematical Sciences in October 1998. This suggests the risk that the book is a mélange of dated papers of strictly academic interest. Happily, nothing could be further from the truth. This book allows a reader equipped only with basic ideas of modern risk management to advance rapidly to the frontiers of research in this area. Perhaps because the editor has selected as authors a good mix of practitioners and academics, the book is useful to both groups of finance researchers. Value at Risk (VaR) quantifies the maximum amount, with probability x, that a portfolio can lose. That is, (1 − x) of the time one expects portfolio losses to exceed the VaR. The book opens with Picoult's paper " Quantifying the Risk of Trading " , which describes the fundamentals of VaR-based risk analysis. It focuses on valuation uncertainty, market risk, and counterparty credit risk. The final chapter of the book, Medova and Kyriacou's " Extremes in Operational Risk Management " , adds a mathematical framework for analyzing risks associated with human error or fraud, system breakdowns, or other external factors such as natural disasters. Three other contributions, of particular interest to the mathematician, describe modern modifications to and improvement of VaR, including the incorporation tail loss estimators, problems with correlations and their replacement by the copula technique, and extreme value statistics. Those thinking that innovations such as these make VaR obsolete are disabused of the notion by chapter 2, " Value at Risk Analysis of a Leveraged Swap " , by Sanjay Srivastava. This chapter described how application of basic VaR techniques could have kept Proctor & Gamble out of a spectacularly unsuccessful pair of interest rate swap trades. Kupiec contributes a chapter focusing on the important problem of " Stress Testing in a Value at Risk Framework ". Stress testing is a way of exploring the effect of possible scenarios on an investment portfolio. The scenarios may be generated by looking at past financial market crises (such as that around the devaluation of the Thai Baht), either by assuming that past correlations between asset prices remain invariant or by introducing volatility and correlation shocks. Value at Risk presents many computational challenges. It is particularly difficult to determine the VaR of a large, complicated portfolio whose positions …