Copyright © 2015 by Matt Sekerke. All rights reserved.

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       Library of Congress Cataloging-in-Publication Data:

      Sekerke, Matt.

      Bayesian risk management: a guide to model risk and sequential learning in financial markets / Matt Sekerke.

      pages cm. – (The Wiley finance series)

      Includes bibliographical references and index.

      ISBN 978-1-118-70860-6 (cloth) – ISBN 978-1-118-74745-2 (epdf) – ISBN 978-1-118-74750-6 (epub)

      1. Finance – Mathematical models. 2. Financial risk management – Mathematical models. 3. Bayesian statistical decision theory. I. Title.

      HG106.S45 2015

      332′.041501519542–dc23

      2015013791

      Cover Design: Wiley

      Cover Image: Abstract background © iStock.com/matdesign24

      Preface

      Most financial risk models assume that the future will look like the past. They don't have to. This book sketches a more flexible risk-modeling approach that more fully recognizes our uncertainty about the future.

      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.

      The core concern of this book is to present and justify alternative tools to measure financial risk without assuming that time-invariant stochastic processes drive financial phenomena. Discarding time-invariance as a modeling assumption makes uncertainty about parameters, models, and forecasts accessible and irreducible in a way that standard statistical risk measurements do not. The constructive alternative offered here under the slogan Bayesian Risk Management is an online sequential Bayesian modeling framework that acknowledges all of these sources of uncertainty, without giving up the structure afforded by parametric risk models and asset-pricing models.

      Following an introductory chapter on the far-reaching consequences of the time-invariance assumption, Part One of the book shows where Bayesian analysis opens up uncertainty about parameters and models in a static setting. Bayesian results are compared to standard statistical results to make plain the strong assumptions embodied in classical, “objective” statistics. Chapter 2 begins by discussing prior information and parameter uncertainty in the context of the binomial and normal linear regression models. I compare Bayesian results to classical results to show how the Bayesian approach nests classical statistical results as a special case, and relate prior distributions under the Bayesian framework to hypothesis tests in classical statistics as competing methods of introducing nondata information. Chapter 3 addresses uncertainty about models and shows how candidate models may be compared to one another. Particular focus is given to the relationship between prior information and model complexity, and the manner in which model uncertainty applies to asset-pricing models.

       Part Two extends the Bayesian framework to sequential time series analysis. Chapter 4 introduces the practice of discounting as a means of creating adaptive models. Discounting reflects uncertainty about the degree of continuity between the past and the future, and prevents the accumulation of data from destroying model flexibility. Expanding the set of available models to entertain multiple candidate discount rates incorporates varying degrees of memory into the modeling enterprise, avoiding the need for an a priori view about the rate at which market information decays. Chapters 5 and 6 then develop the fundamental tools of sequential Bayesian time series analysis: dynamic linear models and sequential Monte Carlo (SMC) models. Each of these tools incorporates parameter uncertainty, model uncertainty, and information decay into an online filtering framework, enabling real-time learning about financial market conditions.

       Part Three then applies the methods developed in the first two parts to the estimation of volatility in Chapter 7