定量风险管理—贝叶斯在金融中的应用（英文版书）

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定量风险管理—贝叶斯在金融中的应用（英文版书）
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Contents

  Preface xv
About the Authors xvii
CHAPTER 1
Introduction 1
A Few Notes on Notation 3
Overview 4
CHAPTER 2
The Bayesian Paradigm 6
The Likelihood Function 6
The Poisson Distribution Likelihood Function 7
The Normal Distribution Likelihood Function 9
The Bayes’ Theorem 10
Bayes’ Theorem and Model Selection 14
Bayes’ Theorem and Classification 14
Bayesian Inference for the Binomial Probability 15
Summary 21
CHAPTER 3
Prior and Posterior Information, Predictive Inference 22
Prior Information 22
Informative Prior Elicitation 23
Noninformative Prior Distributions 25
Conjugate Prior Distributions 27
Empirical Bayesian Analysis 28
Posterior Inference 30
Posterior Point Estimates 30
Bayesian Intervals 32
Bayesian Hypothesis Comparison 32
Bayesian Predictive Inference 34
Illustration: Posterior Trade-off and the Normal Mean
Parameter 35
Summary 37
Appendix: Definitions of Some Univariate and Multivariate
Statistical Distributions 38
The Univariate Normal Distribution 39
The Univariate Student’s t-Distribution 39
The Inverted χ2 Distribution 39
The Multivariate Normal Distribution 40
The Multivariate Student’s t-Distribution 40
The Wishart Distribution 41
The Inverted Wishart Distribution 41
CHAPTER 4
Bayesian Linear Regression Model 43
The Univariate Linear Regression Model 43
Bayesian Estimation of the Univariate Regression
Model 45
Illustration: The Univariate Linear Regression Model 53
The Multivariate Linear Regression Model 56
Diffuse Improper Prior 58
Summary 60
CHAPTER 5
Bayesian Numerical Computation 61
Monte Carlo Integration 61
Algorithms for Posterior Simulation 63
Rejection Sampling 64
Importance Sampling 65
MCMC Methods 66
Linear Regression with Semiconjugate Prior 77
Approximation Methods: Logistic Regression 82
The Normal Approximation 84
The Laplace Approximation 89
Summary 90
CHAPTER 6
Bayesian Framework For Portfolio Allocation 92
Classical Portfolio Selection 94
Portfolio Selection Problem Formulations 95

Mean-Variance Efficient Frontier 97
Illustration: Mean-Variance Optimal Portfolio
with Portfolio Constraints 99
Bayesian Portfolio Selection 101
Prior Scenario 1: Mean and Covariance with Diffuse
(Improper) Priors 102
Prior Scenario 2: Mean and Covariance with Proper
Priors 103
The Efficient Frontier and the Optimal Portfolio 105
Illustration: Bayesian Portfolio Selection 106
Shrinkage Estimators 108
Unequal Histories of Returns 110
Dependence of the Short Series on the Long Series 112
Bayesian Setup 112
Predictive Moments 113
Summary 116
CHAPTER 7
Prior Beliefs and Asset Pricing Models 118
Prior Beliefs and Asset Pricing Models 119
Preliminaries 119
Quantifying the Belief About Pricing Model Validity 121
Perturbed Model 121
Likelihood Function 122
Prior Distributions 123
Posterior Distributions 124
Predictive Distributions and Portfolio Selection 126
Prior Parameter Elicitation 127
Illustration: Incorporating Confidence about the
Validity of an Asset Pricing Model 128
Model Uncertainty 129
Bayesian Model Averaging 131
Illustration: Combining Inference from the CAPM and
the Fama and French Three-Factor Model 134
Summary 135
Appendix A: Numerical Simulation of the Predictive
Distribution 135
Sampling from the Predictive Distribution 136
Appendix B: Likelihood Function of a Candidate Model 138

CHAPTER 8
The Black-Litterman Portfolio Selection Framework 141
Preliminaries 142
Equilibrium Returns 142
Investor Views 144
Distributional Assumptions 144
Combining Market Equilibrium and Investor Views 146
The Choice of τ and
147
The Optimal Portfolio Allocation 148
Illustration: Black-Litterman Optimal Allocation 149
Incorporating Trading Strategies into the Black-Litterman
Model 153
Active Portfolio Management and the Black-Litterman
Model 154
Views on Alpha and the Black-Litterman Model 157
Translating a Qualitative View into a Forecast for
Alpha 158
Covariance Matrix Estimation 159
Summary 161
CHAPTER 9
Market Efficiency and Return Predictability 162
Tests of Mean-Variance Efficiency 164
Inefficiency Measures in Testing the CAPM 167
Distributional Assumptions and Posterior
Distributions 168
Efficiency under Investment Constraints 169
Illustration: The Inefficiency Measure, R 170
Testing the APT 171
Distributional Assumptions, Posterior and Predictive
Distributions 172
Certainty Equivalent Returns 173
Return Predictability 175
Posterior and Predictive Inference 177
Solving the Portfolio Selection Problem 180
Illustration: Predictability and the Investment Horizon 182
Summary 183
Appendix: Vector Autoregressive Setup 183

CHAPTER 10
Volatility Models 185
Garch Models of Volatility 187
Stylized Facts about Returns 188
Modeling the Conditional Mean 189
Properties and Estimation of the GARCH(1,1) Process 190
Stochastic Volatility Models 194
Stylized Facts about Returns 195
Estimation of the Simple SV Model 195
Illustration: Forecasting Value-at-Risk 198
An Arch-Type Model or a Stochastic Volatility Model? 200
Where Do Bayesian Methods Fit? 200
CHAPTER 11
Bayesian Estimation of ARCH-Type Volatility Models 202
Bayesian Estimation of the Simple GARCH(1,1) Model 203
Distributional Setup 204
Mixture of Normals Representation of the Student’s
t-Distribution 206
GARCH(1,1) Estimation Using the
Metropolis-Hastings Algorithm 208
Illustration: Student’s t GARCH(1,1) Model 211
Markov Regime-switching GARCH Models 214
Preliminaries 215
Prior Distributional Assumptions 217
Estimation of the MS GARCH(1,1) Model 218
Sampling Algorithm for the Parameters of the MS
GARCH(1,1) Model 222
Illustration: Student’s t MS GARCH(1,1) Model 222
Summary 225
Appendix: Griddy Gibbs Sampler 226
Drawing from the Conditional Posterior Distribution
of ν 227
CHAPTER 12
Bayesian Estimation of Stochastic Volatility Models 229
Preliminaries of SV Model Estimation 230
Likelihood Function 231
The Single-Move MCMC Algorithm for SV Model
Estimation 232

Prior and Posterior Distributions 232
Conditional Distribution of the Unobserved Volatility 233
Simulation of the Unobserved Volatility 234
Illustration 236
The Multimove MCMC Algorithm for SV Model Estimation 237
Prior and Posterior Distributions 237
Block Simulation of the Unobserved Volatility 239
Sampling Scheme 241
Illustration 241
Jump Extension of the Simple SV Model 241
Volatility Forecasting and Return Prediction 243
Summary 244
Appendix: Kalman Filtering and Smoothing 244
The Kalman Filter Algorithm 244
The Smoothing Algorithm 246
CHAPTER 13
Advanced Techniques for Bayesian Portfolio Selection 247
Distributional Return Assumptions Alternative to Normality 248
Mixtures of Normal Distributions 249
Asymmetric Student’s t-Distributions 250
Stable Distributions 251
Extreme Value Distributions 252
Skew-Normal Distributions 253
The Joint Modeling of Returns 254
Portfolio Selection in the Setting of Nonnormality:
Preliminaries 255
Maximization of Utility with Higher Moments 256
Coskewness 257
Utility with Higher Moments 258
Distributional Assumptions and Moments 259
Likelihood, Prior Assumptions, and Posterior
Distributions 259
Predictive Moments and Portfolio Selection 262
Illustration: HLLM’s Approach 263
Extending The Black-Litterman Approach: Copula Opinion
Pooling 263
Market-Implied and Subjective Information 264
Views and View Distributions 265
Combining the Market and the Views:The Marginal
Posterior View Distributions 266

Views Dependence Structure:The Joint Posterior View
Distribution 267
Posterior Distribution of the Market Realizations 267
Portfolio Construction 268
Illustration: Meucci’s Approach 269
Extending The Black-Litterman Approach:Stable
Distribution 270
Equilibrium Returns Under Nonnormality 270
Summary 272
APPENDIX A: Some Risk Measures Employed in Portfolio
Construction 273
APPENDIX B: CVaR Optimization 276
APPENDIX C: A Brief Overview of Copulas 277
CHAPTER 14
Multifactor Equity Risk Models 280
Preliminaries 281
Statistical Factor Models 281
Macroeconomic Factor Models 282
Fundamental Factor Models 282
Risk Analysis Using a Multifactor Equity Model 283
Covariance Matrix Estimation 283
Risk Decomposition 285
Return Scenario Generation 287
Predicting the Factor and Stock-Specific Returns 288
Risk Analysis in a Scenario-Based Setting 288
Conditional Value-at-Risk Decomposition 289
Bayesian Methods for Multifactor Models 292
Cross-Sectional Regression Estimation 293
Posterior Simulations 293
Return Scenario Generation 294
Illustration 294
Summary 295
References 298
Index 311

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