Bayesian Risk Management

MATT SEKERKE is an economic consultant based in New York whose work focuses on the financial services industry and the application of advanced quantitative modeling techniques o financial data. He holds a BA in economics and mathematics from The Johns Hopkins University, an MA in history from The Johns Hopkins University, and an MBA in econometrics and statistics, analytic finance, and entrepreneurship from The University of Chicago Booth School of Business. He is also a CFA charterholder, a certified Financial Risk Manager, and a certified Energy Risk Professional.

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