Hands-On Value-at-Risk and Expected Shortfall

This book describes a maximally simple market risk model that is still practical and main risk measures like the value-at-risk and the expected shortfall. It outlines the model's (i) underlying math, (ii) daily operation, and (iii) implementation, while stripping away statistical overhead to keep the concepts accessible. The author selects and weighs the various model features, motivating the choices under real-world constraints, and addresses the evermore important handling of regulatory requirements. The book targets not only practitioners new to the field but also experienced market risk operators by suggesting useful data analysis procedures and implementation details. It furthermore addresses market risk consumers such as managers, traders, and compliance officers by making the model behavior intuitively transparent.

Autorentext
Martin Auer is senior consultant in the areas of quantitative finance, market and credit risk, and IT, working for the likes of Raiffeisen Bank International, Kommunalkredit, and T-Systems in Vienna, and for Bank of America in New York. He holds degrees in computer science, mathematics, and mathematics of finance from Vienna University of Technology, University of Vienna, and Columbia University.

Inhalt
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11Part I MEASURES3 Basic Terms and Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214 Historical Value-at-Risk . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 295 Sensitivities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 376 Stress Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 437 Analytical Value-at-Risk . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 458 Expected Shortfall . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 499 Model Choices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5110 A Monte Carlo Modification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5911 Support Measures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63Part II OPERATIONS12 Properties of VaR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7113 Properties of ES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7514 VaR Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7915 Backtesting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8356 Contents16 Distribution Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8717 Nine to Five . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93Part III SETUP18 Context . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11119 Scope and Workflow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11520 Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123WRAP-UP21 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13722 Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139APPENDIXA Statistics 101 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141B Pricing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167C Further Reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183