Coherent Stress Testing A Bayesian Approach to the Analysis of Financial Stress

by Rebonato, Riccardo

• ISBN13: 9780470666012
• ISBN10: 0470666013
• Edition: 1st
• Format: Hardcover
• Copyright: 2010-07-13
• Publisher: Wiley

Summary

Why a book about stress testing? And why a book about stress testing now? Stress testing has been part of the risk manager's toolkit for decades. What justifies the renewed interest from practitioners and regulators for a risk management tool that has always been the poor relation in the family of analytical techniques to control risk? And why has stress testing so far been regarded as a second-class citizen? Understanding the reason for the renewed interest is simple: the financial crisis of 2007-2009 has shown with painful clarity the limitations of the purely statistical techniques (such as VaR and Economic Capital) that were supposed to provide the cornerstones of the financial edifice. As once in a lifetime events kept on occurring with disconcerting regularity in the twenty-or-so months starting with July 2007, it became clear that something new was required.Stress Testing: A Coherent Approach presents groundbreaking new approaches to stress testing. Acknowledged industry expert Riccardo Rebonato moves beyond economic capital and VaR approaches to stress testing to offer a new approach to this risk management discipline. The book sets out by looking at the existing models and how they are used (and abused) by the risk manager. It then moves on to look at the different probabilistic approaches that can be taken in the measurement of risk, at well known and less well known quantitative approaches for stress testing, linear programming, before proposing a new approach to stress testing. Finally, the book sets all of the above in the context of financial institution and a new era of regulation and governance.

Author Biography

DR. RICCARDO REBONATO (London, UK) is Head of Front Office Risk Management and Head of the Clients Analytics team at BGM RBS. He is visiting lecturer at Oxford University (Mathematical Finance) and adjunct professor at Imperial College (Tanaka Business School). He sits on the Board of Directors of ISDA and on the Board of Trustees for GARP. He is an editor for the International Journal of Theoretical and Applied Finance, Applied Mathematical Finance, Journal of Risk, and the Journal of Risk Management in Financial Institutions. He holds doctorates in Nuclear Engineering and in Science of Material/Solid State Phsyics. He was a research fellow in Physics at Corpus Christi College, Oxford, UK.

Table of Contents

Acknowledgements

Introduction

Why We Need Stress Testing

Plan of the Book

Suggestions for Further Reading

Data, Models and Reality

Risk and Uncertainty - or, Why Stress Testing is Not Enough

The Limits of Quantitative Risk Analysis

Risk or Uncertainty?

Suggested Reading

The Role of Models in Risk Management and Stress Testing

How Did We Get Here?

Statement of the Two Theses of this Chapter

Defence of the First Thesis (Centrality of Models)

Models as Indispensable Interpretative Tools

The Plurality-of-Models View

Defence of the Second Thesis (Coordination)

Traders as Agents

Agency Brings About Coordination

From Coordination to Positive Feedback

The Role of Stress and Scenario Analysis

Suggestions for Further Reading

What Kind of Probability Do We Need in Risk Management?

Frequentist versus Subjective Probability

Tail Co-dependence

From Structural Models to Co-dependence

Association or Causation?

Suggestions for Further Reading

The Probabilistic Tools and Concepts

Probability with Boolean Variables I: Marginal and Conditional Probabilities

The Set-up and What We are Trying to Achieve

(Marginal) Probabilities

Deterministic Causal Relationship

Conditional Probabilities

Time Ordering and Causation

An Important Consequence: Bayes' Theorem

Independence

Two Worked-Out Examples

Dangerous Running

Rare and Even More Dangerous Diseases

Marginal and Conditional Probabilities: A Very Important Link

Interpreting and Generalizing the Factors xk i

Conditional Probability Maps

Probability with Boolean Variables II: Joint Probabilities

Conditioning on More Than One Event

Joint Probabilities

A Remark on Notation

From the Joint to the Marginal and the Conditional Probabilities

From the Joint Distribution to Event Correlation

From the Conditional and Marginal to the Joint Probabilities?

Putting Independence to Work

Conditional Independence

Obtaining Joint Probabilities with Conditional Independence

At a Glance

Summary

Suggestions for Further Reading

Creating Probability Bounds

The Lay of the Land

Bounds on Joint Probabilities

How Tight are these Bounds in Practice?

Bayesian Nets I: An Introduction

Bayesian Nets: An Informal Definition

Defining the Structure of Bayesian Nets

More About Conditional Independence

What Goes in the Conditional Probability Tables?

Useful Relationships

A Worked-Out Example

A Systematic Approach

What Can We Do with Bayesian Nets?

Unravelling the Causal Structure

Estimating the Joint Probabilities

Suggestions for Further Reading

Bayesian Nets II: Constructing Probability Tables

Statement of the Problem

Marginal Probabilities - First Approach

Starting from a Fixed Probability

Starting from a Fixed Magnitude of the Move

Marginal Probabilities - Second Approach

Handling Events of Different Probability

Conditional Probabilities: A Reasonable Starting Point

Conditional Probabilities: Checks and Constraints

Necessary Conditions

Triplet Conditions

Independence

Deterministic Causation

Incompatibility of Events

Internal Compatibility of Conditional Probabilities: The Need for a Systematic Approach

Applications

Obtaining a Coherent Solution I: Linear Programming

Plan of the Work Ahead

Coherent Solution with Conditional Probabilities Only

The Methodology in Practice: First Pass

The CPU Cost of the Approach

Illustration of the Linear Programming Technique

What Can We Do with this Information?

Extracting Information with Conditional Probabilities Only

Extracting Information with Conditional and Marginal Probabilities

Obtaining a Coherent Solution II: Bayesian Nets

Solution with Marginal and n-conditioned Probabilities

Generalizing the Results

An 'Automatic' Prescription to Build Joint Probabilities

What Can We Do with this Information?

Risk-Adjusting Returns

Making It Work In Practice

Overcoming Our Cognitive Biases

Cognitive Shortcomings and Bounded Rationality

How Pervasive are Cognitive Shortcomings?

The Social Context

Adaptiveness

Representativeness

Quantification of the Representativeness Bias

Causal/Diagnostic and Positive/Negative Biases

Conclusions

Suggestions for Further Reading

Selecting and Combining Stress Scenarios

Bottom Up or Top Down?

Relative Strengths and Weaknesses of the Two Approaches

Possible Approaches to a Top-Down Analysis

Sanity Checks

How to Combine Stresses - Handling the Dimensionality Curse

Combining the Macro and Bottom-Up Approaches

Governance

The Institutional Aspects of Stress Testing

Transparency and Ease of Use

Challenge by Non-specialists

Checks for Completeness

Interactions among Different Specialists

Auditability of the Process and of the Results

Lines of Criticism

The Role of Subjective Inputs

The Complexity of the Stress-testing Process

Simple Introduction to Linear Programming

Plan of the Appendix

Linear Programming - A Refresher

The Simplex Method

References

Index

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