F.J.ファボッツィ(共)著/金融のためのベイズ法<br>Bayesian Methods in Finance (Frank J Fabozzi Series)

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Bayesian Methods in Finance (Frank J Fabozzi Series)

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  • 製本 Hardcover:ハードカバー版/ページ数 329 p.
  • 言語 ENG
  • 商品コード 9780471920830
  • DDC分類 332.01519542

Full Description

Bayesian Methods in Finance provides a detailed overview of the theory of Bayesian methods and explains their real-world applications to financial modeling. While the principles and concepts explained throughout the book can be used in financial modeling and decision making in general, the authors focus on portfolio management and market risk management-since these are the areas in finance where Bayesian methods have had the greatest penetration to date.

Table of 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 15
Summary 21
CHAPTER 3 Prior and Posterior Information, 22
Predictive Inference
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 35
Normal Mean Parameter
Summary 37
Appendix: Definitions of Some Univariate and 38
Multivariate Statistical Distributions
The Univariate Normal Distribution 39
The Univariate Student's t-Distribution 39
The Inverted x2 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 45
Regression Model
Illustration: The Univariate Linear 53
Regression Model
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 92
Classical Portfolio Selection 94
Portfolio Selection Problem Formulations 95
Mean-Variance Efficient Frontier 97
Illustration: Mean-Variance Optimal 99
Portfolio with Portfolio Constraints
Bayesian Portfolio Selection 101
Prior Scenario 1: Mean and Covariance with 102
Diffuse (Improper) Priors
Prior Scenario 2: Mean and Covariance with 103
Proper Priors
The Efficient Frontier and the Optimal 105
Illustration: Bayesian Portfolio Selection 106
Shrinkage Estimators 108
Unequal Histories of Returns 110
Dependence of the Short Series on the Long 112
Bayesian Setup 112
Predictive Moments 113
Summary 116
CHAPTER 7 Prior Beliefs and Asset Pricing 118
Prior Beliefs and Asset Pricing Models 119
Preliminaries 119
Quantifying the Belief About Pricing Model 121
Perturbed Model 121
Likelihood Function 122
Prior Distributions 123
Posterior Distributions 124
Predictive Distributions and Portfolio 126
Prior Parameter Elicitation 127
Illustration: Incorporating Confidence 128
about the Validity of an Asset Pricing Model
Model Uncertainty 129
Bayesian Model Averaging 131
Illustration: Combining Inference from the 134
CAPM and the Fama and French Three-Factor
Summary 135
Appendix A: Numerical Simulation of the 135
Predictive Distribution
Sampling from the Predictive Distribution 136
Appendix B: Likelihood Function of a 138
Candidate Model
CHAPTER 8 The Black-Litterman Portfolio 141
Selection Framework
Preliminaries 142
Equilibrium Returns 142
Investor Views 144
Distributional Assumptions 144
Combining Market Equilibrium and Investor 146
The Choice of τ and Ω 147
The Optimal Portfolio Allocation 148
Illustration: Black-Litterman Optimal 149
Incorporating Trading Strategies into the 153
Black-Litterman Model
Active Portfolio Management and the 154
Black-Litterman Model
Views on Alpha and the Black-Litterman Model 157
Translating a Qualitative View into a 158
Forecast for Alpha
Covariance Matrix Estimation 159
Summary 161
CHAPTER 9 Market Efficiency and Return 162
Tests of Mean-Variance Efficiency 164
Inefficiency Measures in Testing the CAPM 167
Distributional Assumptions and Posterior 968
Efficiency under Investment Constraints 169
Illustration: The Inefficiency Measure, 170
Testing the APT 171
Distributional Assumptions, Posterior and 172
Predictive Distributions
Certainty Equivalent Returns 173
Return Predictability 175
Posterior and Predictive Inference 177
Solving Me Portfolio Selection Problem 180
Illustration: Predictability and the 182
Investment Horizon
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) 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 200
Where Do Bayesian Methods Fit? 200
CHAPTER 11 Bayesian Estimation of ARCH-Type 202
Volatility Models
Bayesian Estimation of the Simple GARCH(1,1) 203
Distributional Setup 204
Mixture of Normals Representation of the 206
Student's t-Distribution
GARCH(1,1) Estimation Using the 208
Metropolis-Hastings Algorithm
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 222
the MS GARCH(1,1) Model
Illustration: Student's t MS GARCH(1,1) 222
Summary 225
Appendix: Griddy Gibbs Sampler 226
Drawing from the Conditional Posterior 227
Distribution of v
CHAPTER 12 Bayesian Estimation of Stochastic 229
Volatility Models
Preliminaries of SV Model Estimation 230
Likelihood Function 231
The Single-Move MCMC Algorithm for SV Model 232
Prior and Posterior Distributions 232
Conditional Distribution of the Unobserved 233
Simulation of the Unobserved Volatility 234
Illustration 236
The Multimove MCMC Algorithm for SV Model 237
Prior and Posterior Distributions 237
Block Simulation of the Unobserved 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 247
Portfolio Selection
Distributional Return Assumptions Alternative 248
to Normality
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 255
Nonnormality: Preliminaries
Maximization of Utility with Higher Moments 256
Coskewness 257
Utility with Higher Moments 258
Distributional Assumptions and Moments 259
Likelihood, Prior Assumptions, and 259
Posterior Distributions
Predictive Moments and Portfolio Selection 262
Illustration: HLLM's Approach 263
Extending The Black-Litterman Approach: 263
Copula Opinion Pooling
Market-Implied and Subjective Information 264
Views and View Distributions 265
Combining the Market and the Views: The 266
Marginal Posterior View Distributions
Views Dependence Structure: The Joint 267
Posterior View Distribution
Posterior Distribution of the Market 267
Portfolio Construction 268
Illustration: Meucci's Approach 269
Extending The Black-Litterman Approach: 270
Stable Distribution
Equilibrium Returns Under Nonnormality 270
Summary 272
APPENDIX A: Some Risk Measures Employed in 273
Portfolio Construction
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 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