Bayesian Risk Management: A Guide to Model Risk and Sequential Learning in Financial Markets

A Risk Measurement and Management Framework that Takes Model Risk Seriously

Why do risk models break down? The answer may lie in the way that statistical methods are conventionally used to draw inferences about market conditions and inform risk–taking behavior. Bayesian Risk Management enables a discussion on the way standard statistical methods overlook uncertainty in model specifications, model parameters, and model–driven forecasts. In a simple and direct way, Bayesian methods are used throughout the book to:

Recognize the assumptions embodied in classical statistics Quantify model risk along multiple dimensions Model time–series without assuming continuity between past and future Adjust time–series estimates to maintain forecast accuracy Uncover uncertainty in workhorse risk and asset–pricing models Achieve decentralized control of risk–taking in complex organizations

For firms in financial services and other industries operating in a dynamic environment of incomplete information, Bayesian Risk Management provides a thought–provoking challenge to the prevailing wisdom about the uses and limitations of statistical risk modeling.

Preface

Acknowledgments

Chapter 1: Models for Discontinuous Markets

Risk Models and Model Risk

Time–Invariant Models and Crisis

Bayesian Probability as a Means of Handling Discontinuity

Time–Invariance and Objectivity

Part One: Capturing Uncertainty in Statistical Models

Chapter 2: Prior Knowledge, Parameter Uncertainty, and Estimation

Estimation with Prior Knowledge: The Beta–Bernoulli Model

Prior Parameter Distributions as Hypotheses: The Normal Linear Regression Model

Decisions after Observing the Data: The Choice of Estimators

Chapter 3: Model Uncertainty

Bayesian Model Comparison

Models as Nuisance Parameters

Uncertainty in Pricing Models

A Note on Backtesting

Part Two: Sequential Learning with Adaptive Statistical Models

Chapter 4: Introduction to Sequential Modeling

Sequential Bayesian Inference

Achieving Adaptivity via Discounting

Accounting for Uncertainty in Sequential Models

State Space Models of Time Series

Dynamic Linear Models

Recursive Relationships in the DLM

Variance Estimation

Sequential Model Comparison

Chapter 5: Sequential Monte Carlo Inference

Non–Linear and Non–Normal Models

State Learning with Particle Filters

Joint Learning of Parameters and States

Sequential Model Comparison

Part Three: Sequential Models of Financial Risk

Chapter 6: Volatility Modeling

Single–Asset Volatility

Volatility for Multiple Assets

Chapter 7: Asset Pricing Models and Hedging

Derivative Pricing in the Schwartz Model

Online State–Space Model Estimates of Derivative Prices

Models for Portfolios of Assets

Part Four: Bayesian Risk Management

Chapter 8: From Risk Measurement to Risk Management

Results

Prior Information as an Instrument of Corporate Governance

References

Index

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.