Quantitative Financial Risk Management

A mathematical guide to measuring and managing financial risk.

Our modern economy depends on financial markets. Yet financial markets continue to grow in size and complexity. As a result, the management of financial risk has never been more important.

Quantitative Financial Risk Management introduces students and risk professionals to financial risk management with an emphasis on financial models and mathematical techniques. Each chapter provides numerous sample problems and end of chapter questions. The book provides clear examples of how these models are used in practice and encourages readers to think about the limits and appropriate use of financial models.

Topics include:

• Value at risk
• Stress testing
• Credit risk
• Liquidity risk
• Factor analysis
• Expected shortfall
• Copulas
• Extreme value theory
• Risk model backtesting
• Bayesian analysis
• . . . and much more

Preface vii

About the Author ix

1 Overview of Financial Risk Management 1

2 Market Risk: Standard Deviation 15

3 Market Risk: Value at Risk 51

4 Market Risk: Expected Shortfall, and Extreme ValueTheory 73

5 Market Risk: Portfolios and Correlation 91

6 Market Risk: Beyond Correlation 119

7 Market Risk: Risk Attribution 151

8 CreditRisk 167

9 Liquidity Risk 189

10 Bayesian Analysis 205

11 Behavioral Economics and Risk 231

Appendix A Maximum Likelihood Estimation 247

Appendix B Copulas 253

Answers to End-of-Chapter Questions 257

References 295

Index 297

MICHAEL B. MILLER is the founder and CEO of Northstar Risk Corp. Before starting Northstar, Mr. Miller was Chief Risk Officer for Tremblant Capital and, before that, Head of Quantitative Risk Management at Fortress Investment Group.

Mr. Miller is the author of Mathematics and Statistics for Financial Risk Management, now in its second edition, and, along with Emanuel Derman, The Volatility Smile. He is also an adjunct professor at Columbia University and the co-chair of the Global Association of Risk Professional’s Research Fellowship Committee. Before starting his career in finance, Mr. Miller studied economics at the American University of Paris and the University of Oxford.

From the bestselling author of Mathematics and Statistics for Financial Risk Management comes this must-have guide to Quantitative Financial Risk Management

Our modern economy depends on financial markets, yet financial markets continue to grow in size and complexity. As a result, the management of financial risk has never been more important.

Quantitative Financial Risk Management is a textbook designed to teach students about financial risk management with an emphasis on financial models and mathematical techniques. Each chapter provides numerous sample problems and end-of-chapter questions. The book provides clear examples of how these models are used in practice and encourages students to think about the limits and appropriate use of financial risk models.

Topics covered include:

• Value at risk
• Stress testing
• Credit risk
• Liquidity risk
• Factor analysis
• Expected shortfall
• Copulas
• Extreme value theory
• Risk model backtesting
• Risk attribution
• Bayesian analysis
• and much more…

Quantitative Financial Risk Management is a practitioner’s textbook. Michael B. Miller draws on his own experience working in the financial industry and teaching to provide a book that is both rigorous and practical.

Each chapter explores a particular topic in risk management along with various mathematical tools that can be used to understand that topic. In addition, each chapter includes a number of sample problems and end-of-chapter questions. Over the course of the book, students gain an appreciation for the challenges that risk managers face in modeling financial securities and portfolios.