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

by Riccardo Rebonato (Royal Bank of Scotland Group)

• ISBN13: 9780470667361
• ISBN10: 0470667362
• Format: eBook
• Copyright: 2010-05-01
• Publisher: Wiley

Summary

In Coherent Stress Testing: A Bayesian Approach, industry expert Riccardo Rebonato presents a groundbreaking new approach to this important but often undervalued part of the risk management toolkit.Based on the author's extensive work, research and presentations in the area, the book fills a gap in quantitative risk management by introducing a new and very intuitively appealing approach to stress testing based on expert judgement and Bayesian networks. It constitutes a radical departure from the traditional statistical methodologies based on Economic Capital or Extreme-Value-Theory approaches.The book is split into four parts. Part I looks at stress testing and at its role in modern risk management. It discusses the distinctions between risk and uncertainty, the different types of probability that are used in risk management today and for which tasks they are best used. Stress testing is positioned as a bridge between the statistical areas where VaR can be effective and the domain of total Keynesian uncertainty. Part II lays down the quantitative foundations for the concepts described in the rest of the book. Part III takes readers through the application of the tools discussed in part II, and introduces two different systematic approaches to obtaining a coherent stress testing output that can satisfy the needs of industry users and regulators. In part IV the author addresses more practical questions such as embedding the suggestions of the book into a viable governance structure.

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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