C. Alexander: Market Risk Analysis (four-volume set)

Abstract

It is highly doubtful whether there could be a more appropriate time to release this four-volume set, Market Risk Analysis, by Carol Alexander, since the current financial crisis has demonstrated the need (and, sometimes, inability) to understand the risks resulting from adverse movements in the prices of financial instruments. Even though the author of this impressive work often mentions and refers to risk management, the series is rightly called Market Risk Analysis because the focus is on mathematical ways to model and analyze market risks, a necessary prerequisite for managing such risks. The series consists of four books with many cross-references and consistent notation throughout, but each book is self-contained and can be purchased and read separately. Volume 1 provides the essential mathematical and financial background needed to understand the concepts introduced in the other three volumes. There are six chapters in Volume 1, one each on calculus, linear algebra (including a very enticing treatment of principal component analysis, or PCA), probability and statistics, linear regression, numerical methods, and portfolio mathematics. Of course, there are many other books solely devoted to each of these topics by itself, but the way in which the author provides an introduction to such vast topics and covers so much ground in a concise but never superficial way in a single volume deserves special praise. Even if you are not at all interested in market risk analysis but simply want a clear overview of quantitative models employed in finance, you can make good use of this book. The second volume deals with financial econometrics from a practical point of view, focusing on time-series econometrics. Over the course of eight chapters, the reader is introduced to factor models, PCA, models of volatility and correlation, GARCH models, cointegration, and copulas. As the author is a mathematician by