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

InhaltsangabePreface 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 OneFactor Gaussian Copula (OFGC) ModelToo 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? 1

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