Elements of Financial Risk Management, Second Edition

science......Page 2
Elements of Financial Risk Management......Page 3
Copyright......Page 4
Dedication......Page 5
New in the Second Edition......Page 11
Organization of the Book......Page 12
Acknowledgments......Page 13
2 Learning Objectives......Page 15
3.1 Why Should Firms Manage Risk?......Page 16
3.3 Does Risk Management Improve Firm Performance?......Page 17
4 A Brief Taxonomy of Risks......Page 18
5 Asset Returns Definitions......Page 19
6 Stylized Facts of Asset Returns......Page 21
7 A Generic Model of Asset Returns......Page 23
9 Introducing the Value-at-Risk (VaR) Risk Measure......Page 24
10 Overview of the Book......Page 28
A Return VaR and $VaR......Page 29
References......Page 30
Empirical Exercises......Page 31
2 Historical Simulation......Page 33
2.2 Pros and Cons of Historical Simulation......Page 34
3 Weighted Historical Simulation (WHS)......Page 36
4 Evidence from the 2008–2009 Crisis......Page 40
5 The True Probability of Breaching the HS VaR......Page 43
6 VaR with Extreme Coverage Rates......Page 44
7 Expected Shortfall......Page 45
8 Summary......Page 48
References......Page 49
Empirical Exercises......Page 50
1 Chapter Overview......Page 51
2.1 Univariate Probability Distributions......Page 52
2.2 Bivariate Distributions......Page 54
2.3 Conditional Distributions......Page 55
2.4 Sample Moments......Page 56
3 The Linear Model......Page 57
3.1 The Importance of Data Plots......Page 58
4 Univariate Time Series Models......Page 60
4.1 Autocorrelation......Page 61
4.2 Autoregressive (AR) Models......Page 62
4.3 Moving Average (MA) Models......Page 66
4.4 Combining AR and MA into ARMA Models......Page 67
4.5 Random Walks, Units Roots, and ARIMA Models......Page 69
4.7 Testing for Unit Roots......Page 70
5.2 Pitfall 2: Spurious Regression......Page 71
5.3 Cointegration......Page 72
5.5 Vector Autoregressions (VAR)......Page 73
6 Summary......Page 74
References......Page 75
Empirical Exercises......Page 76
1 Chapter Overview......Page 77
2 Simple Variance Forecasting......Page 78
3 The GARCH Variance Model......Page 80
4.1 Standard Maximum Likelihood Estimation......Page 83
4.3 An Example......Page 85
5.1 The Leverage Effect......Page 86
5.2 More General News Impact Functions......Page 87
5.3 More General Dynamics......Page 88
5.4 Explanatory Variables......Page 90
5.5 Generalizing the Low Frequency Variance Dynamics......Page 91
6.1 Model Comparisons Using LR Tests......Page 92
6.2 Diagnostic Check on the Autocorrelations......Page 93
6.4 The Volatility Forecast Loss Function......Page 94
Appendix A: Component GARCH and GARCH(2,2)\r......Page 96
Appendix B: The HYGARCH Long-Memory Model\r......Page 98
References......Page 99
Empirical Exercises......Page 101
1 Chapter Overview......Page 103
2 Realized Variance: Four Stylized Facts......Page 104
3.1 Simple ARMA Models of Realized Variance......Page 108
3.2 Heterogeneous Autoregressions (HAR)......Page 109
3.3 Combining GARCH and RV......Page 112
4.1 The All RV Estimator......Page 113
4.3 The Average RV Estimator......Page 115
4.4 RV Estimators with Autocovariance Adjustments......Page 116
5.1 Dealing with Irregularly Spaced Intraday Prices......Page 117
5.3 Dealing with Data Gaps from Overnight Market Closures......Page 118
5.4 Alternative RV Estimators Using Tick-by-Tick Data......Page 119
6 Range-Based Volatility Modeling......Page 120
6.1 Range-Based Proxies for Volatility......Page 121
6.2 Forecasting Volatility Using the Range......Page 123
7 GARCH Variance Forecast Evaluation Revisited......Page 125
Further Resources......Page 126
References......Page 127
Empirical Exercises......Page 129
2 Learning Objectives......Page 131
3 Visualizing Nonnormality Using QQ Plots......Page 133
4 The Filtered Historical Simulation Approach......Page 134
5 The Cornish-Fisher Approximation to VaR......Page 136
6 The Standardized t Distribution......Page 138
6.1 Maximum Likelihood Estimation......Page 139
6.2 An Easy Estimate of d......Page 140
6.3 Calculating Value-at-Risk and Expected Shortfall......Page 141
6.4 QQ Plots......Page 142
7 The Asymmetric t Distribution......Page 143
7.1 Estimation of d1 and d2......Page 144
7.2 Calculating Value-at-Risk and Expected Shortfall......Page 146
8 Extreme Value Theory (EVT)......Page 147
8.1 The Distribution of Extremes......Page 148
8.2 Estimating the Tail Index Parameter, ξ......Page 149
8.4 Constructing the QQ Plot from EVT......Page 150
8.5 Calculating VaR and ES from the EVT Quantile......Page 151
9 Summary......Page 153
Appendix A: ES for the Symmetric and Asymmetric t Distributions\r......Page 154
Appendix B:\rCornish-Fisher ES......Page 155
Appendix C:\rExtreme Value Theory ES......Page 156
References......Page 157
Empirical Exercises......Page 159
1 Chapter Overview......Page 160
2 Portfolio Variance and Covariance......Page 161
2.1 Exposure Mappings......Page 162
2.2 GARCH Conditional Covariances......Page 163
3 Dynamic Conditional Correlation (DCC)......Page 166
3.1 Exponential Smoother Correlations......Page 167
3.2 Mean-Reverting Correlation......Page 168
3.3 Bivariate Quasi Maximum Likelihood Estimation......Page 170
3.4 Composite Likelihood Estimation in Large Systems......Page 171
4 Estimating Daily Covariance from Intraday Data......Page 172
4.1 Realized Covariance......Page 173
4.2 Range-Based Covariance Using No-Arbitrage Conditions......Page 174
5 Summary......Page 175
Further Resources......Page 176
References......Page 177
Empirical Exercises......Page 178
1 Chapter Overview......Page 179
2 The Risk Term Structure in Univariate Models......Page 180
2.1 Monte Carlo Simulation......Page 182
2.2 Filtered Historical Simulation (FHS)......Page 185
3 The Risk Term Structure with Constant Correlations......Page 188
3.2 Multivariate Filtered Historical Simulation......Page 191
4.1 Monte Carlo Simulation with Dynamic Correlations......Page 192
4.2 Filtered Historical Simulation with Dynamic Correlations......Page 194
Further Resources......Page 195
References......Page 196
Empirical Exercises......Page 197
1 Chapter Overview......Page 198
2 Threshold Correlations......Page 199
3 Multivariate Distributions......Page 200
3.1 The Multivariate Standard Normal Distribution......Page 201
3.2 The Multivariate Standardized t Distribution......Page 203
3.3 The Multivariate Asymmetric t Distribution......Page 205
4.1 Sklar\'s Theorem......Page 208
4.2 The Normal Copula......Page 210
4.3 The t Copula......Page 212
5.1 Copula VaR and ES by Simulation......Page 215
5.2 Integrated Risk Management......Page 217
Further Resources......Page 218
References......Page 219
Empirical Exercises......Page 220
1 Chapter Overview......Page 221
2 Basic Definitions......Page 222
3.1 Step 1: Build the Tree for the Stock Price......Page 224
3.2 Step 2: Compute the Option Payoff at Maturity......Page 225
3.3 Step 3: Work Backward in the Tree to Get the Current Option Value......Page 227
3.4 Risk Neutral Valuation......Page 229
3.5 Pricing an American Option Using the Binomial Tree......Page 230
4 Option Pricing under the Normal Distribution......Page 232
4.2 Implied Volatility......Page 235
5 Allowing for Skewness and Kurtosis......Page 237
5.1 Model Implementation......Page 239
6 Allowing for Dynamic Volatility......Page 241
6.1 Model Implementation......Page 243
6.2 A Closed-Form GARCH Option Pricing Model......Page 245
7 Implied Volatility Function (IVF) Models......Page 246
Appendix: The CFG Option Pricing Formula\r......Page 247
Further Resources......Page 249
References......Page 250
Empirical Exercises......Page 251
1 Chapter Overview......Page 253
2 The Option Delta......Page 254
2.1 The Black-Scholes-Merton Model......Page 255
2.2 The Binomial Tree Model......Page 257
2.4 The GARCH Option Pricing Models......Page 258
3 Portfolio Risk Using Delta......Page 259
4 The Option Gamma......Page 261
5 Portfolio Risk Using Gamma......Page 263
5.1 The Cornish-Fisher Approximation......Page 264
5.2 The Simulation-Based Gamma Approximation......Page 265
6.1 The Single Underlying Asset Case......Page 267
6.2 The General Case......Page 268
7 A Simple Example......Page 269
8 Pitfall in the Delta and Gamma Approaches......Page 273
Further Resources......Page 275
References......Page 276
Empirical Exercises......Page 277
1 Chapter Overview......Page 278
2 A Brief History of Corporate Defaults......Page 279
3 Modeling Corporate Default......Page 281
3.1 Equity Is a Call Option on the Assets of the Firm......Page 282
3.2 Corporate Debt Is a Put Option Sold......Page 283
3.3 Implementing the Model......Page 284
4 Portfolio Credit Risk......Page 285
4.2 The Portfolio Loss Rate Distribution......Page 287
4.4 Granularity Adjustment......Page 289
5.1 Recovery Rates......Page 291
5.2 Credit Quality Dynamics......Page 293
5.3 Credit Default Swaps......Page 295
Further Resources......Page 296
References......Page 297
Empirical Exercises......Page 298
1 Chapter Overview......Page 300
2.1 The Null Hypothesis......Page 302
2.2 Unconditional Coverage Testing......Page 303
2.3 Independence Testing......Page 305
2.5 Testing for Higher-Order Dependence......Page 307
3 Increasing the Information Set......Page 308
4 Backtesting Expected Shortfall......Page 309
5 Backtesting the Entire Distribution......Page 310
5.1 Backtesting Only the Left Tail of the Distribution......Page 312
6 Stress Testing......Page 313
6.1 Combining Distributions for Coherent Stress Testing......Page 314
6.2 Choosing Scenarios......Page 315
6.3 Stress Testing the Term Structure of Risk......Page 316
7 Summary......Page 317
Further Resources......Page 318
References......Page 319
Empirical Exercises......Page 320
C......Page 322
F......Page 323
L......Page 324
P......Page 325
S......Page 326
W......Page 327