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Correlation Risk Modeling and Management: An Applied Guide including the Basel III Correlation Framework - With Interactive Models in Excel / VBA, + Website


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

GUNTER MEISSNER, PH.D., heads Dersoft (, 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., 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.

Preface xiii

Acknowledgments xvii

About the Author xix

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

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

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

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

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

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

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

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

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

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

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

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

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