Probabilistic Graphical Models

Alexander Denev

Alexander Denev

Alexander Denev has more than ten years of experience in Finance in different countries across Europe and is the founder of GraphRisk, a company aimed at promoting the use of graphical models in risk management and asset allocation, and senior advisor to Risk Dynamics. He is involved in projects preparing major US and European banks for the CCAR/EBA stress testing exercises.

Alexander led the wholesale modelling team responsible for stress testing of the Royal Bank of Scotland (RBS) until 2014. He was also in charge of the EAD/LGD wholesale modelling teams. Prior to that, he worked in RBS as a fixed income structurer leading the bank’s tail hedging project. He provided advice and devised hedging products for big institutional clients (pension funds and insurance companies). Before joining RBS, Alexander was in charge of the Basel II/III implementation project for the European Investment Bank (EIB) and European Investment Fund (EIF). He was also leading the stress testing exercises both for the EIB and the EIF. He participated in the engineering of both the European Financial Stability Facility and the European Stability Mechanism. Prior to that, he covered different specialist and managerial positions in risk management departments in different large international groups, such as the National Bank of Greece, Société Générale and BNP Paribas.

Alexander holds a degree in mathematical finance from the University of Oxford. He also holds a BSc and MSc in engineering physics from the University of Rome. He is author of papers in finance on topics ranging from stresstesting to asset allocation. He is a regular speaker at key conferences and global forums and is co-author of the book Portfolio Management under Stress.

PART I

INTRODUCTION TO PROBABILISTIC GRAPHICAL MODELS

1         Background and Motivation

1.1 Previous Research: Bayesian Nets

1.2 Challenges and Extensions of Bayesian Nets

1.3 Some Problems faced by the Finance Modelling Community

1.4 Some Problems with the Governance and Use of Models in Institutions

1.5 What We Propose

1.6 Where We Can Learn From

1.7 Some Common Risk Metrics

1.8 A Set of Simple Econometric Models

1.9 Many Models, Many Errors

1.10 Definition and Notation

1.11 Software Tools

11.12 Conclusions

2         Probabilistic Graphical Models: An Introduction

2.1 What Are Probabilistic Graphical Models?

2.2 Probabilistic Graphical Models: A Taxonomy

2.3 Specifying a Probabilistic Graphical Model

2.4 How to Derive the Joint Probability Distribution

2.5 Equivalence

2.6 Causality and Associations

2.7 Which Type of Probabilistic Graphical Model to Select

2.8 The Process of Building a Scenario through a Probabilistic Graphical Model

2.9 The Causal Markov Condition

2.10 Directed Cyclic Graphs

2.11 Continuous Nodes

2.12 Gaussian Networks

2.13 Dynamic Bayesian Nets

2.14 The Problem of Inference

2.15 The Problem of Learning

2.16 Some Additional Simplification

2.17 Conclusions

3         Probabilistic Graphical Models: Filling in the Information

3.1 “Objective” Sources of Information

3.2 Expert and Other Input

3.3 Historical Data

3.4 Market-Implied Information

3.5 Conclusions

PART II APPLICATIONS

4         Stress Testing

4.1 Regulations in Banking and Stress Testing

4.2 Market and Credit Risk Stress Tests: Specific

4.3 “Sticky” Institutional Set-Ups

4.4 A Systemic Stress Test

4.5 Systemic Reverse Stress Tests

4.6 Stress Testing New and Complex Asset Classes

4.7 Regulatory Stress Tests: Bottom-Up

4.8 Conclusions

5         Asset Allocation

5.1 Background

5.2 Some Facts about Financial Time Series

5.3 How We Can Use Probabilistic Graphical Models in Asset Allocation

5.4 How to Model Nil States

5.5 How to Combine the Nil State with the Excited States

5.6 The Problem of Asset Allocation

5.7 Case Study: Liability-Driven Investment

5.8 Conclusions

6         Credit Risk in Loan Portfolios

6.1 Credit Factors and Defaults

6.2 Credit Portfolio Models

6.3 Single-Obligor Models

6.4 Conclusion

7         Financial Networks

7.1 Description of the Network

7.2 A Markov Random Field Approach

7.3 A Directed Cyclic Graphs Approach

7.4 A Gaussian Markov Random Field Approach

7.5 A Bayesian Net Approach

7.6 Dynamic Bayesian Nets and Temporal Aggregation

7.7 Conclusions

8         Hedging

8.1 Some Background

8.2 An Initial Example

8.3 The Single Hedge Case

8.4 The Multiple Hedge Case

8.5 Real-World Example

8.6 Studying the Components

8.7 Hedging under Extreme Scenarios

8.8 Efficient Hedging

8.9 Hybrids

8.10 Conclusions

9         Case Study: When a Country Is Split

9.1 Context

9.2 The “No” Vote

9.3 Notation

9.4 The “Yes” Vote

9.5 Sensitivity and Other Analyses

9.6 Conclusions

10         Case Study: The Impact of an Interest Rate Hike on Mortgage Default Rates

10.1 The Building Blocks of the Analysis

10.2 The Central Bank Rate

10.3 The Housing Market in the UK

10.4 The House hold Sector

10.5 Impact on the Portfolio

10.6 Reverse Stress Testing

10.7 Sensitivity Analyses

10.8 Conclusions