The VaR implementation handbook

538 Pages·2009·3.522 MB·English

by  Greg N Gregoriou

THE VaR
IMPLEMENTATION
HANDBOOK
GREG N. GREGORIOU
EDITOR
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C O N T E N T S
EDITOR xv
CONTRIBUTORS xvii
PART ONE
VaR MEASUREMENT
Chapter 1
Calculating VaR for Hedge Funds 3
Monica Billio,Mila Getmansky,and Loriana Pelizzon
Introduction 4
Hedge Funds 5
Value at Risk 6
Data 13
Results and Discussion 14
Conclusion 20
References 20
Appendix: Strategic Decisions 22
Chapter 2
Efficient VaR: Using Past Forecast Performance to
Generate Improved VaR Forecasts 25
Kevin Dowd and Carlos Blanco
Introduction 25
ABacktesting Framework 27
Using Backtest Results to Recalibrate the Parameters of the VaR Model 29
Some Examples 31
Conclusion 36
References 37
Appendix 38
v
vi Contents
Chapter 3
Applying VaR to Hedge Fund Trading Strategies:
Limitations and Challenges 41
R. McFall Lamm,Jr.
Introduction 41
Background 43
Analytical Approach 44
Application Considerations 46
Impact of VaR Control 47
Short versus Long History for Setting VaR Risk Limits 51
Implications 53
Conclusion 55
References 56
Chapter 4
Cash Flow at Risk: Linking Strategy and Finance 59
Ulrich Hommel
Introduction 59
AProcess View of the Corporate Risk Management Function 62
Value-Based Motives of Firm-Level Risk Management 66
The Incompatibility of Simple Value at Risk with
Corporate Risk Management 70
Operationalizing CFaR 72
Governance Implications 78
Conclusion 80
References 81
Chapter 5
Plausible Operational Value-at-Risk Calculations for
Management Decision Making 85
Wilhelm Kross,Ulrich Hommel,and Martin Wiethuechter
Introduction 85
Operational Risk under Basel II 86
Desirable Side Effects of Operational Risk Initiatives 91
Toward Strategy-Enhancing Operational Risk Initiatives 95
Employment of Real Option Techniques in Operational Risk Initiatives 99
Contents vii
Conclusion 102
References 103
Chapter 6
Value-at-Risk Performance Criterion:A Performance
Measure for Evaluating Value-at-Risk Models 105
Zeno Adams and Roland Füss
Introduction 106
Value-at-RiskPerformance Criterion (VPC) 107
Effects of Changing Volatility and Return Distribution 109
Conclusion 115
References 119
Chapter 7
Explaining Cross-Sectional Differences in Credit
Default Swap Spreads:An Alternative Approach
Using Value at Risk 121
Bastian Breitenfellner and Niklas Wagner
Introduction 122
Estimation Methodology 126
Data and Explanatory Variables 128
Empirical Results 131
Conclusion 135
References 135
Chapter 8
Some Advanced Approaches to VaR Calculation
and Measurement 139
François-Éric Racicot and Raymond Théoret
Introduction 139
Parametric VaR and the Normal Distribution 141
Using Historical Simulation to Compute VaR 142
The Delta Method for Computing VaR 145
The Monte Carlo Simulation 147
The Bootstrapping Method 149
Cornish-Fisher Expansion and VaR 155
viii Contents
Value at Risk for a Distribution Other Than the Normal but
Using a Normal Coefficient 156
Copulas, Fourier’s Transform, and the VaR 157
Conclusion 162
References 163
Chapter 9
Computational Aspects of Value at Risk 167
Germán Navarro and Ignacio Olmeda
Introduction 168
Supercomputing Technologies 169
Graphics Processing Unit Computing 171
An Example 174
Conclusion 182
References 182
PART 2
RISK AND ASSET MANAGEMENT
Chapter 10
Value-at-Risk–Based Stop-Loss Trading 187
Bernd Scherer
Introduction 188
Stop-Loss Rules for Alternative Return Processes 189
Some Well-known Strategies 192
Conditional Autocorrelation: Threshold Autoregressive Models 196
Conclusion 202
References 203
Appendix: Currency Universe and Data Availability 205
Chapter 11
Modeling Portfolio Risks with Time-Dependent
Default Rates in Venture Capital 207
Andreas Kemmerer,Jan Rietzschel,and Henry Schoenball
Introduction 208
Contents ix
Initial Model 208
Risk Modeling with Time-Dependent Default Rates 215
Empirical Evidence 220
Conclusion 226
References 226
Chapter 12
Risk Aggregation and Computation of Total Economic Capital 229
Peter Grundke
Introduction 229
Additive Approach 232
Correlation-Based Square-Root Formula 232
Top-Down Approach 233
Bottom-Up Approach 240
Conclusion 241
References 247
Chapter 13
Value at Risk for High-Dimensional Portfolios:
A Dynamic Grouped t-Copula Approach 253
Dean Fantazzini
Introduction 254
Dynamic Grouped t-Copula Modeling: Definition and Estimation 256
Simulation Studies 259
Empirical Analysis 271
Conclusion 277
References 279
Appendix: List of Analyzed Stocks 282
Chapter 14
A Model to Measure Portfolio Risks in Venture Capital 283
Andreas Kemmerer
Introduction 284
Toward a Risk Model in Venture Capital 285
ARisk Model for Venture Capital 290
x Contents
Data Sample 297
Empirical Evidence 299
Conclusion 308
References 308
Chapter 15
Risk Measures and Their Applications in Asset Management 311
S. Ilker Birbil,Hans Frenk,Bahar Kaynar,and Nilay Noyan
Introduction 312
Risk Measures 315
ASingle-Period Portfolio Optimization Problem 320
Elliptical World 324
Modified Michelot Algorithm 328
Computational Results 331
Conclusion 336
References 336
Chapter 16
Risk Evaluation of Sectors Traded at the ISE
with VaR Analysis 339
Mehmet Orhan and Gökhan Karaahmet
Introduction 339
Value-at-Risk Comparison of Sectors Traded at the
Istanbul Stock Exchange (ISE) 343
Performance of VaR in Evaluating Risk 350
Conclusion 356
References 357
PART THREE
MODELING
Chapter 17
Aggregating and Combining Ratings 361
Rafael Weißbach,Frederik Kramer,and Claudia Lawrenz
Introduction 362
Contents xi
Mathematical Background 364
Aggregating Ratings 365
Impact Studies 367
Conclusion 379
References 381
Chapter 18
Risk-Managing the Uncertainty in VaR Model Parameters 385
Jason C. Hsu and Vitali Kalesnik
The Subprime Crisis of 2008 386
Parameter Uncertainty 389
An Illustrative Example with Mean Uncertainty 390
An Illustrative Example with Variance Uncertainty 394
An Illustrative Example with Correlation Uncertainty 396
Conclusion 398
Acknowledgment 400
References 400
Chapter 19
Structural Credit Modeling and Its Relationship
To Market Value at Risk:An Australian Sectoral
Perspective 403
David E. Allen and Robert Powell
Introduction 404
Structural Model 406
Methodology 407
Results 410
Conclusion 412
References 412
Chapter 20
Model Risk in VAR Calculations 415
Peter Schaller
Introduction 415
Sources of Model Risk 416
xii Contents
Backtesting 420
Bias versus Uncertainty 422
Pivotal Quantile Estimates 428
Applications 432
Conclusion 436
References 436
Chapter 21
Option Pricing with Constant and
Time-Varying Volatility 439
Willi Semmler and Karim M. Youssef
Introduction 439
The Black Scholes PDE 441
Solution Methods 444
What We Get and What We Do Not Get from Black Scholes 447
Seeking Sigma 448
Historical Volatility 449
GARCH(1,1) 450
Heston’s Volatility 452
The Heston Valuation Equation 453
Calibrating the Heston Parameters and Results 457
Conclusion 460
References 460
Chapter 22
Value at Risk under Heterogeneous Investment
Horizons and Spatial Relations 463
Viviana Fernandez
Introduction 464
Methodological Issues 466
Empirical Testing of Spatial Linkages 471
Conclusion 480
References 481