Description
Book SynopsisA comprehensive and accessible introduction to modern quantitative risk management. The business world is rife with risk and uncertainty, and risk management is a vitally important topic for managers. The best way to achieve a clear understanding of risk is to use quantitative tools and probability models.
Table of ContentsPreface xiii
1 What is risk management? 1
1.1 Introduction 2
1.2 Identifying and documenting risk 5
1.3 Fallacies and traps in risk management 7
1.4 Why safety is different 9
1.5 The Basel framework 11
1.6 Hold or hedge? 12
1.7 Learning from a disaster 13
Notes 17
References 18
Exercises 19
2 The structure of risk 22
2.1 Introduction to probability and risk 23
2.2 The structure of risk 25
2.3 Portfolios and diversification 30
2.4 The impact of correlation 40
2.5 Using copulas to model multivariate distributions 49
Notes 58
References 59
Exercises 60
3 Measuring risk 63
3.1 How can we measure risk? 64
3.2 Value at risk 67
3.3 Combining and comparing risks 73
3.4 VaR in practice 76
3.5 Criticisms of VaR 79
3.6 Beyond value at risk 82
Notes 88
References 88
Exercises 89
4 Understanding the tails 92
4.1 Heavy-tailed distributions 93
4.2 Limiting distributions for the maximum 100
4.3 Excess distributions 109
4.4 Estimation using extreme value theory 115
Notes 121
References 122
Exercises 123
5 Making decisions under uncertainty 125
5.1 Decisions, states and outcomes 126
5.2 Expected Utility Theory 130
5.3 Stochastic dominance and risk profiles 148
5.4 Risk decisions for managers 156
Notes 160
References 161
Exercises 162
6 Understanding risk behavior 164
6.1 Why decision theory fails 165
6.2 Prospect Theory 172
6.3 Cumulative Prospect Theory 180
6.4 Decisions with ambiguity 189
6.5 How managers treat risk 191
Notes 194
References 194
Exercises 195
7 Stochastic optimization 198
7.1 Introduction to stochastic optimization 199
7.2 Choosing scenarios 212
7.3 Multistage stochastic optimization 218
7.4 Value at risk constraints 224
Notes 228
References 228
Exercises 229
8 Robust optimization 232
8.1 True uncertainty: Beyond probabilities 233
8.2 Avoiding disaster when there is uncertainty 234
8.3 Robust optimization and the minimax approach 250
Notes 261
References 262
Exercises 263
9 Real options 265
9.1 Introduction to real options 266
9.2 Calculating values with real options 267
9.3 Combining real options and net present value 273
9.4 The connection with financial options 278
9.5 Using Monte Carlo simulation to value real options 282
9.6 Some potential problems with the use of real options 285
Notes 287
References 287
Exercises 288
10 Credit risk 291
10.1 Introduction to credit risk 292
10.2 Using credit scores for credit risk 294
10.3 Consumer credit 301
10.4 Logistic regression 308
Notes 317
References 318
Exercises 319
Appendix A Tutorial on probability theory 323
A.1 Random events 323
A.2 Bayes’ rule and independence 326
A.3 Random variables 327
A.4 Means and variances 329
A.5 Combinations of random variables 332
A.6 The normal distribution and the Central Limit Theorem 336
Appendix B Answers to even-numbered exercises 340
Index 361
