Bayesian risk management : a guide to model risk and sequential learning in financial markets

Content: Preface ix     Acknowledgments xiii     CHAPTER 1 Models for Discontinuous Markets 1     Risk Models and Model Risk 2     Time-Invariant Models and Crisis 3     Ergodic Stationarity in Classical Time Series Analysis 5     Recalibration Does Not Overcome the Limits of a     Time-Invariant Model 7     Bayesian Probability as a Means of Handling Discontinuity 8     Accounting for Parameter and Model Uncertainty 9     Responding to Changes in the Market Environment 12     Time-Invariance and Objectivity 14     PART ONE Capturing Uncertainty in Statistical Models     CHAPTER 2 Prior Knowledge, Parameter Uncertainty, and Estimation 19     Estimation with Prior Knowledge: The Beta-Bernoulli Model 20     Encoding Prior Knowledge in the Beta-Bernoulli Model 21     Impact of the Prior on the Posterior Distribution 23     Shrinkage and Bias 24     Efficiency 25     Hyperparameters and Sufficient Statistics 30     Conjugate Prior Families 31     Prior Parameter Distributions as Hypotheses: The Normal Linear Regression Model 31     Classical Analysis of the Normal Linear Regression Model 32     Estimation 32     Hypothesis Testing 34     Bayesian Analysis of the Normal Linear Regression Model 35     Hypothesis Testing with Parameter Distributions 39     Comparison 41     Decisions after Observing the Data: The Choice of Estimators 42     Decisions and Loss 43     Loss and Prior Information 44     CHAPTER 3 Model Uncertainty 47     Bayesian Model Comparison 49     Bayes Factors 49     Marginal Likelihoods 50     Parsimony 52     Bayes Factors versus Information Criteria 53     Bayes Factors versus Likelihood Ratios 54     Models as Nuisance Parameters 55     The Space of Models 56     Mixtures of Models 58     Uncertainty in Pricing Models 58     Front-Office Models 59     The Statistical Nature of Front-Office Models 61     A Note on Backtesting 62     PART TWO Sequential Learning with Adaptive Statistical Models     CHAPTER 4 Introduction to Sequential Modeling 67     Sequential Bayesian Inference 68     Achieving Adaptivity via Discounting 71     Discounting in the Beta-Bernoulli Model 73     Discounting in the Linear Regression Model 77     Comparison with the Time-Invariant Case 81     Accounting for Uncertainty in Sequential Models 83     CHAPTER 5 Bayesian Inference in State-Space Time Series Models 87     State-Space Models of Time Series 88     The Filtering Problem 90     The Smoothing Problem 91     Dynamic Linear Models 94     General Form 94     Polynomial Trend Components 95     Seasonal Components 96     Regression Components 98     Building DLMs with Components 98     Recursive Relationships in the DLM 99     Filtering Recursion 99     Smoothing Recursion 102     Predictive Distributions and Forecasting 104     Variance Estimation 105     Univariate Case 106     Multivariate Case 107     Sequential Model Comparison 108     CHAPTER 6 Sequential Monte Carlo Inference 111     Nonlinear and Non-Normal Models 113     Gibbs Sampling 113     Forward-Filtering Backward-Sampling 114     State Learning with Particle Filters 116     The Particle Set 117     A First Particle Filter: The Bootstrap Filter 117     The Auxiliary Particle Filter 119     Joint Learning of Parameters and States 120     The Liu-West Filter 122     Improving Efficiency with Sufficient Statistics 124     Particle Learning 125     Sequential Model Comparison 126     PART THREE Sequential Models of Financial Risk     CHAPTER 7 Volatility Modeling 131     Single-Asset Volatility 132     Classical Models with Conditional Volatility 132     Rolling-Window-Based Methods 133     GARCH Models 136     Bayesian Models 138     Volatility Modeling with the DLM 139     State-Space Models of Stochastic Volatility 140     Comparison 141     Volatility for Multiple Assets 144     EWMA and Inverted-Wishart Estimates 144     Decompositions of the Covariance Matrix 148     Time-Varying Correlations 149     CHAPTER 8 Asset-Pricing Models and Hedging 155     Derivative Pricing in the Schwartz Model 156     State Dynamics 157     Describing Futures Prices as a Function of Latent Factors 157     Continuous- and Discrete-Time Factor Dynamics 158     Model-Implied Prices and the Observation Equation 161     Online State-Space Model Estimates of Derivative Prices 162     Estimation with the Liu-West Filter 163     Prior Information 165     Estimation Results 166     Estimation Results with Discounting 176     Hedging with the Time-Varying Schwartz Model 188     Connection with Term-Structure Models 190     Models for Portfolios of Assets 191     PART FOUR Bayesian Risk Management     CHAPTER 9 From Risk Measurement to Risk Management 195     Results 195     Time Series Analysis without Time-Invariance 196     Preserving Prior Knowledge 196     Information Transmission and Loss 198     Bayesian State-Space Models of Time Series 199     Real-Time Metrics for Model Risk 200     Adaptive Estimates without Recalibration 202     Prior Information as an Instrument of Corporate Governance 204     References 207  Index 213