Bayesian Risk Management

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Sekerke Matt. Bayesian Risk Management

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

Chapter 5. Bayesian Inference in State-Space Time Series Models

State-Space Models of Time Series

Dynamic Linear Models

Recursive Relationships in the DLM

Variance Estimation

Sequential Model Comparison

Chapter 6. Sequential Monte Carlo Inference

Nonlinear 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 7. Volatility Modeling

Single-Asset Volatility

Volatility for Multiple Assets

Chapter 8. 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 9. From Risk Measurement to Risk Management

Results

Prior Information as an Instrument of Corporate Governance

References

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MATT SEKERKE

Uncertainty about the future stems from our limited ability to specify risk models, estimate their parameters from data, and be assured of the continuity between today's markets and tomorrow's markets. Ignoring any of these dimensions of model risk creates an illusion of mastery and fosters erroneous decision making. It is typical for financial firms to ignore all of these sources of uncertainty. Because they measure too little risk, they take on too much risk.

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The second experience was my involvement in the early stages of litigation related to the credit crisis. In these lawsuits, a few questions were on everyone's mind. Could the actors in question have seen significant changes in the market coming? If so, at what point could they have known that a collapse was imminent? If not, what would have led them to believe that the future was either benign or unknowable? The opportunity to review confidential information obtained in the discovery phase of these litigations provided innumerable insights into the inner workings of the key actors with respect to risk measurement, risk management, and financial instrument valuation. I saw two main things. First, there was an overwhelming dependence on front-office information – bid sheets, a few consummated secondary-market trades, and an overwhelming amount of “market color,” the industry term for the best rumor and innuendo on offer – and almost no dependence on middle-office modeling. Whereas certain middle-office modeling efforts could have reacted to changes in market conditions, the traders on the front lines would not act until they saw changes in traded prices. Second, there were interminable discussions about how to weigh new data on early-stage delinquencies, default rates, and home prices against historical data. Instead of asking whether the new data falsified earlier premises on which expectations were built, discussions took place within the bounds of the worst-known outcomes from history, with the unstated assurance that housing market phenomena were stable and mean-reverting overall. Whatever these observations might imply about the capacity of the actors involved, it seemed that a better balance could be struck between middle-office risk managers and front-office traders, and that gains could be had by making the expectations of all involved explicit in the context of models grounded in the relevant fundamentals.

However, it was not until I began my studies at the University of Chicago that these themes converged around the technical means necessary to make them concrete. Nick Polson's course in probability theory was a revelation, introducing the Bayesian approach to probability within the context of financial markets. Two quarters of independent study with him followed immediately in which he introduced me to the vanguard of Bayesian thinking about time series. A capstone elective on Bayesian econometrics with Hedibert Lopes provided further perspective and rigor. His teaching was a worthy continuation of a tradition at the University of Chicago going back to Arnold Zellner.

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