Correlation Risk Modeling and ManagementAn Applied Guide including the Basel III Correlation Framework - With Interactive Models in Excel / VBA
Wiley Finance 1. Aufl.
A thorough guide to correlation risk and its growing importance in global financial markets Ideal for anyone studying for CFA, PRMIA, CAIA, or other certifications, Correlation Risk Modeling and Management is the first rigorous guide to the topic of correlation risk. A relatively overlooked type of risk until it caused major unexpected losses during the financial crisis of 2007 through 2009, correlation risk has become a major focus of the risk management departments in major financial institutions, particularly since Basel III specifically addressed correlation risk with new regulations. This offers a rigorous explanation of the topic, revealing new and updated approaches to modelling and risk managing correlation risk. Offers comprehensive coverage of a topic of increasing importance in the financial world Includes the Basel III correlation framework Features interactive models in Excel/VBA, an accompanying website with further materials, and problems and questions at the end of each chapter
Preface xiii Acknowledgments xvii About the Author xix CHAPTER 1 Some Correlation Basics: Properties, Motivation, Terminology 1 1.1 What Are Financial Correlations? 1 1.2 What Is Financial Correlation Risk? 2 1.3 Motivation: Correlations and Correlation Risk Are Everywhere in Finance 5 1.4 How Does Correlation Risk Fit into the Broader Picture of Risks in Finance? 24 1.5 A Word on Terminology 33 1.6 Summary 34 Appendix 1A: Dependence and Correlation 35 Dependence 35 Correlation 36 Independence and Uncorrelatedness 37 Appendix 1B: On Percentage and Logarithmic Changes 38 Practice Questions and Problems 39 References and Suggested Readings 40 CHAPTER 2 Empirical Properties of Correlation: How Do Correlations Behave in the Real World? 43 2.1 How Do Equity Correlations Behave in a Recession, Normal Economic Period, or Strong Expansion? 43 2.2 Do Equity Correlations Exhibit Mean Reversion? 46 2.3 Do Equity Correlations Exhibit Autocorrelation? 50 2.4 How Are Equity Correlations Distributed? 51 2.5 Is Equity Correlation Volatility an Indicator for Future Recessions? 52 2.6 Properties of Bond Correlations and Default Probability Correlations 53 2.7 Summary 54 Practice Questions and Problems 55 References and Suggested Readings 55 CHAPTER 3 Statistical Correlation Models—Can We Apply Them to Finance? 57 3.1 AWord on Financial Models 57 3.2 Statistical Correlation Measures 60 3.3 Should We Apply Spearman’s Rank Correlation and Kendall’s t in Finance? 65 3.4 Summary 66 Practice Questions and Problems 67 References and Suggested Readings 68 CHAPTER 4 Financial Correlation Modeling—Bottom-Up Approaches 69 4.1 Correlating Brownian Motions (Heston 1993) 69 4.2 The Binomial CorrelationMeasure 72 4.3 Copula Correlations 74 4.4 Contagion Correlation Models 88 4.5 Summary 90 Appendix 4A: Cholesky Decomposition 91 Example: Cholesky Decomposition for Three Assets 92 Appendix 4B: A Short Proof of the Gaussian Default Time Copula 93 Practice Questions and Problems 93 References and Suggested Readings 94 CHAPTER 5 Valuing CDOs with the Gaussian Copula—What Went Wrong? 101 5.1 CDO Basics—What Is a CDO? Why CDOs? Types of CDOs 101 5.2 Valuing CDOs 105 5.3 Conclusion: The Gaussian Copula and CDOs—What Went Wrong? 113 5.4 Summary 115 Practice Questions and Problems 116 References and Suggested Readings 117 CHAPTER 6 The One-Factor Gaussian Copula (OFGC) Model—Too Simplistic? 119 6.1 The Original One-Factor Gaussian Copula (OFGC) Model 121 6.2 Valuing Tranches of a CDO with the OFGC 122 6.3 The Correlation Concept in the OFGC Model 128 6.4 The Relationship between the OFGC and the Standard Copula 131 6.5 Extensions of the OFGC 132 6.6 Conclusion—Is the OFGC Too Simplistic to Evaluate Credit Risk in Portfolios? 135 6.7 Summary 138 Practice Questions and Problems 139 References and Suggested Readings 140 CHAPTER 7 Financial Correlation Models—Top-Down Approaches 143 7.1 Vasicek’s 1987 One-Factor Gaussian Copula (OFGC) Model Revisited 144 7.2 Markov Chain Models 146 7.2.1 Inducing Correlation via Transition Rate Volatilities 146 7.3 Contagion Default Modeling in Top-Down Models 150 7.4 Summary 153 Practice Questions and Problems 154 References and Suggested Readings 154 CHAPTER 8 Stochastic Correlation Models 157 8.1 What Is a Stochastic Process? 157 8.2 Sampling Correlation from a Distribution (Hull and White 2010) 159 8.3 Dynamic Conditional Correlations (DCCs) (Engle 2002) 160 8.4 Stochastic Correlation—Standard Models 162 8.5 Extending the Heston Model with Stochastic Correlation (Buraschi et al. 2010; Da Fonseca et al. 2008) 168 8.6 Stochastic Correlation, Stochastic Volatility, and Asset Modeling (Lu and Meissner 2012) 172 8.7 Conclusion: Should We Model Financial Correlations with a Stochastic Process? 176 8.8 Summary 177 Practice Questions and Problems 177 References and Suggested Readings 178 CHAPTER 9 Quantifying Market Correlation Risk 181 9.1 The Correlation Risk Parameters Cora and Gora 182 9.2 Examples of Cora in Financial Practice 184 9.3 Cora and Gora in Investments 187 9.4 Cora in Market Risk Management 189 9.5 Gora in Market Risk Management 197 9.6 Summary 198 Practice Questions and Problems 199 References and Suggested Readings 200 CHAPTER 10 Quantifying Credit Correlation Risk 201 10.1 Credit Correlation Risk in a CDS 203 10.2 Pricing CDSs, Including Reference Entity–Counterparty Credit Correlation 205 10.3 Pricing CDSs, Including the Credit Correlation of All Three Entities 215 10.4 Correlation Risk in a Collateralized Debt Obligation (CDO) 227 10.5 Summary 231 Practice Questions and Problems 232 References and Suggested Readings 233 CHAPTER 11 Hedging Correlation Risk 235 11.1 What Is Hedging? 235 11.2 Why Is Hedging Financial Correlations Challenging? 238 11.3 Two Examples to Hedge Correlation Risk 239 11.4 When to Use Options and When to Use Futures to Hedge 247 11.5 Summary 248 Practice Questions and Problems 249 References and Suggested Readings 249 CHAPTER 12 Correlation and Basel II and III 251 12.1 What Are the Basel I, II, and III Accords? Why Do Most Sovereigns Implement The Accords? 251 12.2 Basel II and III’s Credit Value at Risk (CVaR) Approach 252 12.3 Basel II’s Required Capital (RC) for Credit Risk 258 12.4 Credit Value Adjustment (CVA) Approach without Wrong-Way Risk (WWR) in The Basel Accord 261 12.5 Credit Value Adjustment (CVA) with Wrong-Way Risk in the Basel Accord 264 12.6 How Do the Basel Accords Treat Double Defaults? 269 12.7 Debt Value Adjustment (DVA): If Something Sounds Too Good to Be True . . . 274 12.8 Funding Value Adjustment (FVA) 276 12.9 Summary 278 Practice Questions and Problems 280 References and Suggested Readings 280 CHAPTER 13 The Future of Correlation Modeling 283 13.1 Numerical Finance: Solving Financial Problems Numerically with the Help of Graphical Processing Units (GPUs) 283 13.2 New Developments in Artificial Intelligence and Financial Modeling 287 13.3 Summary 298 Practice Questions and Problems 300 References and Suggested Readings 300 Glossary 303 Index 315
GUNTER MEISSNER, PH.D., heads Dersoft (www.dersoft.com), the software company behind TradeSmart, a software package that derives futures, options, and swaps prices and risk parameters. In addition, he runs a hedge fund (www. cassandracm.com), and is Adjunct Professor of Mathematical Finance at NYU. Dr. Meissner joined Deutsche Bank in 1990, where he traded interest rate futures, swaps, and options in Frankfurt and New York. He became Head of Product Development in 1994, responsible for originating algorithms for new derivatives products. In 1995/1996 Dr. Meissner became Head of Options at Deutsche Bank Tokyo. From 1997 to 2007, he was Professor of Finance at Hawaii Pacific University. From 2008 to 2013 he was Director of the Master in Financial Engineering program at the Shidler College of Business at the University of Hawaii. The author of numerous published papers on derivatives in international journals, Dr. Meissner also is a frequent speaker at international conferences and seminars and the author of four other books, including The Definitive Guide to CDOs: Application, Pricing, and Risk Management.
The risk of financial loss due to unfavorable movements in the correlation between two or more assets, correlation risk is a critical factor in many areas of finance, including trading, investing, portfolio management and regulation. As was vividly demonstrated by the 2007–2009 global financial crisis, correlations also play a vital role in systemic crises, where sudden increases in correlations can lead to devastating losses. As a consequence, over the past several years, correlation risk has become a major focus in the risk management departments of most major financial institutions. In addition, correlation is also the centerpiece of the Basel Accords to derive value at risk (VAR), credit value at risk, (CVAR) and credit value adjustment (CVA). Written by a leading international authority in the field, Correlation Risk Modeling and Management is the first hands-on guide to this increasingly crucial topic. Designed to function as both a working resource for an array of finance professionals, including risk managers, analysts, traders, brokers, compliance officers and controllers, as well as a key student text/study guide, this book: Provides comprehensive, practical coverage of both traditional and new methods and models Includes in-depth coverage of the Basel III correlation risk management framework Explores new correlation risk measures of the Basel III accord, including the Basel's credit risk valuation with correlated wrong-way risk and correlated double defaults. Contains interactive correlation modeling software, in Excel and VBA Features an accompanying website offering a gold mine of additional materials Supplies chapter-end problems and questions that let you test and reinforce your understanding Correlation Risk Management and Modeling is an indispensable resource for anyone with exposure to financial correlations and financial correlation risk. It also is an excellent graduate-level text and a valuable study guide for those preparing to sit for their CFA, PRMIA, CAIA exams or other related certification tests.
Praise for The Definitive Guide to CDOs: Application, Pricing, and Risk Management. "In the past, derivatives researchers have devoted a great deal of effort to modeling volatility, but have not paid enough attention to correlation. The crisis of 2008 showed us just how important correlations can be. This book looks at all aspects of correlation modeling and will be a valuable resource for both academics and practitioners." —John Hull, Maple Financial Professor of Derivatives and Risk Management Joseph L. Rotman School of Management University of Toronto "This book zeroes in on the quantitative issue at the heart of the crisis. We are way past due on a book of this nature." —Peter Carr, PhD., Global Head of Market Modeling, Morgan Stanley Executive Director of the Masters in Math Finance Program, NYU "This book is a very timely and needed reference reviewing the various approaches to correlation modelling from across all areas of OTC derivatives analytics. The author contributed broadly to the subject and the insights he shares will be useful to practitioners and academics alike." —Claudio Albanese, CEO, Global Valuation
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