9780631227090

A step-by-step, real-world guide to the use of Value at Risk (VaR) models, this text applies the VaR approach to the measurement of market risk, credit risk, and operational risk. The book describes and critiques proprietary models, illustrating them with practical examples drawn from actual case studies. Explaining the logic behind the economics and statistics, this technically sophisticated yet intuitive text should be an essential resource for all readers operating in a world of risk. The text uses VaR techniques to analyze loans, derivatives, equity prices, foreign currencies and other financial instruments. Featuring comprehensive coverage of the BIS bank capital requirements, and including the latest proposals for the New Capital Accord, the book also describes the newest application of VaR techniques to operational risk measurement. The text examines the promise and the pitfalls of these risk measurement models, and makes recommendations for future research into this important area.

Linda Allen is Professor of Finance at the Zicklin School of Business at Baruch College, City University of New York, and Adjunct Professor of Finance at the Stern School of Business, New York University. She is also the author of Capital Markets and Institutions: A Global View and co-author of Credit Risk Measurement: New Approaches to Value at Risk and Other Paradigms, (2nd edition). She is an associate editor of the Journal of Banking and Finance, Journal of Economics and Business, and Multinational Finance Journal, and has published extensively in top academic journals in finance and economics.

Jacob Boudoukh is Professor of Finance and the founding director of theCaesarea Edmond Benjamin de Rothschild Center for Capital Markets and Risk Management at the Arison School of Business, IDC; as well as holding positions at the Stern School of Business, New York University. ormerly formerly with and currently visiting Stern-NYU; and a member of the NBER. His work has been published in academic journals such as The American Economic Review, and The Journal of Financial Economics, as well as practitioner journals such as Risk.Anthony Saunders is John M. Schiff Professor of Finance and Chair of the Department of Finance at the Stern School of Business, and Economics and Finance Department Chair at New York University. He is also editor of the Journal of Banking and Finance and the Journal of Financial Markets, Institutions and Instruments, and has published Financial Institutions and Management (2nd4th edition). Professor Saunders has published widely in top journals such as Journal of Finance.

List of Figures

xiv

List of Tables

xvi

Preface

xviii

List of Abbreviations

xx

1 Introduction to Value at Risk (VaR)

1

(20)

1.1 Economics underlying VaR measurement

2

(11)

1.1.1 What is VaR?

4

(2)

1.1.2 Calculating VaR

6

(2)

1.1.3 The assumptions behind VaR calculations

8

(2)

1.1.4 Inputs into VaR calculations

10

(3)

1.2 Diversification and VaR

13

(8)

1.2.1 Factors affecting portfolio diversification

16

(1)

1.2.2 Decomposing volatility into systematic and idiosyncratic risk

17

(1)

1.2.3 Diversification: Words of caution - the case of long-term capital management (LTCM)

18

(3)

2 Quantifying Volatility in VaR Models

21

(61)

2.1 The stochastic Behavior of Returns

22

(13)

2.1.1 Revisiting the assumptions

22

(1)

2.1.2 The distribution of interest rate changes

23

(2)

2.1.3 Fat tails

25

(1)

2.1.4 Explaining fat tails

26

(3)

2.1.5 Effects of volatility changes

29

(2)

2.1.6 Can (conditional) normality be salvaged?

31

(3)

2.1.7 Normality cannot be salvaged

34

(1)

2.2 VaR Estimation Approaches

35

(24)

2.2.1 Cyclical volatility

36

(1)

2.2.2 Historical standard deviation

36

(2)

2.2.3 Implementation considerations

38

(2)

2.2.4 Exponential smoothing - RiskMetrics™ volatility

40

(8)

2.2.4.1 The optimal smoother lambda

43

(1)

2.2.4.2 Adaptive volatility estimation

44

(1)

2.2.4.3 The empirical performance of RiskMetrics™

45

(1)

2.2.4.4 GARCH

45

(3)

2.2.5 Nonparametric volatility forecasting

48

(6)

2.2.5.1 Historical simulation

48

(3)

2.2.5.2 Multivariate density estimation

51

(3)

2.2.6 A comparison of methods

54

(2)

2.2.7 The hybrid approach

56

(3)

2.3 Return Aggregation and VaR

59

(3)

2.4 Implied Volatility as a Predictor of Future Volatility

62

(4)

2.5 Long Horizon Volatility and VaR

66

(3)

2.6 Mean Reversion and Long Horizon Volatility

69

(2)

2.7 Correlation Measurement

71

(3)

2.8 summary

74

(1)

Appendix 2.1 Backtesting Methodology and Results

74

(8)

3 Putting VaR to Work

82

(37)

3.1 The VaR of Derivatives - Preliminaries

82

(15)

3.1.1 Linear derivatives

83

(3)

3.1.2 Nonlinear derivatives

86

(1)

3.1.3 Approximating the VaR of derivatives

86

(7)

3.1.4 Fixed income securities with embedded optionality

93

(2)

3.1.5 "Delta normal" vs. full-revaluation

95

(2)

3.2 structured Monte Carlo, Stress Testing, and scenario Analysis

97

(13)

3.2.1 Motivation

97

(1)

3.2.2 structured Monte Carlo

98

(3)

3.2.3 Scenario analysis

101

(9)

3.2.3.1 Correlation breakdown

101

(2)

3.2.3.2 Generating reasonable stress

103

(1)

3.2.3.3 Stress testing in practice

104

(2)

3.2.3.4 Stress testing and historical simulation

106

(1)

3.2.3.5 Asset concentration

107

(3)

3.3 Worst Case Scenario (WCS)

110

(3)

3.3.1 WCS vs. VaR

110

(1)

3.3.2 A comparison of VaR to WCS

111

(1)

3.3.3 Extensions

112

(1)

3.4 Summary

113

(1)

Appendix 3.1 Duration

114

(5)

4 Extending the VaR Approach to Non-tradable Loans

119

(39)

4.1 Traditional Approaches to Credit Risk Measurement

120

(8)

4.1.1 Expert systems

121

(1)

4.1.2 Rating systems

122

(2)

4.1.3 Credit scoring models

124

(4)

4.2 Theoretical Underpinnings: Two Approaches

128

(10)

4.2.1 Options-theoretic structural models of credit risk measurement

128

(4)

4.2.2 Reduced form or intensity-based models of credit risk measurement

132

(6)

4.2.3 Proprietary VaR models of credit risk measurement

138

(1)

4.3 CreditMetrics

138

(13)

4.3.1 The distribution of an individual loan's value

138

(5)

4.3.2 The value distribution for a portfolio of loans

143

(18)

4.3.2.1 Calculating the correlation between equity returns and industry indices for each borrower in the loan portfolio

144

(1)

4.3.2.2 Calculating the correlation between borrower equity returns

144

(1)

4.3.2.3 Solving for joint migration probabilities

145

(2)

4.3.2.4 Valuing each loan across the entire credit migration spectrum

147

(2)

4.3.2.5 Calculating the mean and standard deviation of the normal portfolio value distribution

149

(2)

4.4 Algorithmics' Mark-to-Future

151

(2)

4.5 Summary

153

(2)

Appendix 4.1 CreditMetrics: Calculating Credit VaR Using the Actual Distribution

155

(3)

5 Extending the VaR Approach to Operational Risks

158

(42)

5.1 Top-Down Approaches to Operational Risk Measurement

161

(9)

5.1.1 Top-down vs. bottom-up models

162

(1)

5.1.2 Data requirements

163

(2)

5.1.3 Top-down models

165

(5)

5.1.3.1 Multi-factor models

165

(1)

5.1.3.2 Income-based models

166

(1)

5.1.3.3 Expense-based models

167

(1)

5.1.3.4 Operating leverage models

167

(1)

5.1.3.5 Scenario analysis

167

(1)

5.1.3.6 Risk profiling models

168

(2)

5.2 Bottom-Up Approaches to Operational Risk Measurement

170

(15)

5.2.1 Process approaches

170

(6)

5.2.1.1 Causal networks or scorecards

170

(3)

5.2.1.2 Connectivity models

173

(2)

5.2.1.3 Reliability models

175

(1)

5.2.2 Actuarial approaches

176

(6)

5.2.2.1 Empirical loss distributions

176

(1)

5.2.2.2 Parametric loss distributions

176

(3)

5.2.2.3 Extreme value theory

179

(3)

5.2.3 Proprietary operational risk models

182

(3)

5.3 Hedging Operational Risk

185

(11)

5.3.1 Insurance

186

(2)

5.3.2 Self-insurance

188

(2)

5.3.3 Hedging using derivatives

190

(5)

5.3.3.1 Catastrophe options

191

(2)

5.3.3.2 Cat bonds

193

(2)

5.3.4 Limitations to operational risk hedging

195

(1)

5.4 Summary

196

(1)

Appendix 5.1 Copula Functions

196

(4)

6 Applying VaR to Regulatory Models

200

(33)

6.1 BIS Regulatory Models of Market Risk

203

(3)

6.1.1 The standardized framework for market risk

203

(2)

6.1.1.1 Measuring interest rate risk

203

(1)

6.1.1.2 Measuring foreign exchange rate risk

204

(1)

6.1.1.3 Measuring equity price risk

205

(1)

6.1.2 Internal models of market risk

205

(1)

6.2 BIS Regulatory Models of Credit Risk

206

(15)

6.2.1 The Standardized Model for credit risk

207

(2)

6.2.2 The Internal Ratings-Based Models for credit risk

209

(6)

6.2.2.1 The Foundation IRB Approach

210

(4)

6.2.2.2 The Advanced IRB Approach

214

(1)

6.2.3 BIS regulatory models of off-balance sheet credit risk

215

(3)

6.2.4 Assessment of the BIS regulatory models of credit risk

218

(3)

6.3 BIS Regulatory Models of Operational Risk

221

(10)

6.3.1 The Basic Indicator Approach

223

(1)

6.3.2 The Standardized Approach

224

(1)

6.3.3 The Advanced Measurement Approach

225

(6)

6.3.3.1 The internal measurement approach

227

(3)

6.3.3.2 The loss distribution approach

230

(1)

6.3.3.3 The scorecard approach

230

(1)

6.4 Summary

231

(2)

7 VaR: Outstanding Research

233

(3)

7.1 Data Availability

233

(1)

7.2 Model Integration

234

(1)

7.3 Dynamic Modeling

235

(1)

Notes

236

(21)

References

257

(13)

Index

270

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Understanding Market, Credit, and Operational Risk The Value at Risk Approach

Understanding Market, Credit, and Operational Risk The Value at Risk Approach

0631227091

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