Probabilistic Graphical Models: A New Way of Thinking in Financial Modelling - Risk Books
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Probabilistic Graphical Models: A New Way of Thinking in Financial Modelling

By Alexander Denev


Probabilistic Graphical Models gives an overview of PGMs (a framework encompassing techniques like bayesian networks, markov random fields and chain graphs), which incorporate forward-looking information for making financial decisions, and applies them to stress testing, asset allocation, hedging, and credit risk.

This approach describes a new way to contend with stress testing (a big component of regulations like CCAR, the AIFMD, and Solvency II), teaches the reader how to strengthen their portfolios, presents a forward-looking way of conducting tail hedging, and gives a clear picture of the credit risk of the institution in question (such as a bank or a hedge fund).

Take a look at the intro here.

Publish date: 22 Jul 2015

Availability: In stock

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Book - Probabilistic Graphical Models: A New Way of Thinking in Financial Modelling

Book description

Probabilistic Graphical Models teaches this relatively new technique to the reader, explaining how it can be applied to a variety of everyday challenges. Previous to their use in finance, PGMs have been used in disciplines such as computer science, engineering and medicine. Author Alexander Denev expands on this pre-existing material to examine other types of PGMs, demonstrating a novel range of applications. 

Chapters feature:

  • Why is a new approach needed?
  • Probabilistic Graphical Models: An Overview
  • Stress Testing
  • Asset Allocation
  • Hedging
  • Credit Risk

Book details

Book - 9781782720973 / eBook - 9781782722465
Publish date
22 Jul 2015
155mm x 235mm

Author biography

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.

Table of contents



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


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


"Scenario generation has become one of the key challenges that banks have had to address since the financial crisis. Regulators have requested banks to come up with their own scenarios consistent with their risk exposures, and also to perform reverse stress testing, i.e.,  finding a particularly severe scenario that could bring down the bank and work back its causes. There is currently no definitive solution to this problem and obviously this is still work in progress. The publication of the book by Alexander Denev, Probabilistic Graphical Models: A New Way of Thinking in Financial Modelling, comes at a perfect time to contribute to the current debate on the appropriate methodological frameworks for scenario generation. Alexander Denev is proposing an original graphical and intuitive approach that uses Bayesian nets to stress testing. Through several examples and case studies Alexander Denev demonstrates that Probabilistic Graphical Models (PGM) are powerful tools for expressing causal relationships. PGMs allows the reader to build forward-looking probability distributions that helps to create forward-looking stress scenarios and to perform reverse stress testing.

This book is definitively a must read book for anyone involved in stress testing whether in the risk management, finance or ALM groups of a financial institution."

Michel Crouhy, Head of Research & Development, Natixis

"Probabilistic Graphical Models by Alex Denev presents real world financial models embedding structural features so as to capture both normal and distressed capital markets.

Building on a graphical framework reflecting the causal links between the model variables, Denev crafts risk management tools where traditional risk methodologies must remain silent: reverse stress testing of financial institutions, multi-asset efficient frontier optimisation and robust macro hedging under tail risk scenarios, default clustering in corporate loans and mortgages, analysing contagion across financial networks, estimating the impact of unique constitutional events.

The models resort to graphical statistical techniques such as static (& dynamic) Bayesian nets to capture causal and temporal connections, Markovian random fields admitting simultaneous and two-way interactions, and directed cyclic graphs for more complicated risk factor topologies, complemented with parsimonious discrete or random probability laws, whilst taking care not to assume structural variety, randomness and irreducible economic uncertainty out of the picture.

Confrontation and calibration of real case studies, taking in not just financial time series and implied market data but richer input from macro-economic modelling and domain expertise, are advocated and illustrated throughout the work.  Denev has written a fresh and welcome counterpoint to the risk-neutral “orthodoxy” of current mathematical finance literature."

Erik Vynckier, Chief Investment Officer (Insurance), AllianceBernstein

"Most econometric methods consist in simple linear algebra applications. These tools are not able to grasp the complexity of modern financial systems. In this book, Alexander Denev introduces a novel practical approach where hierarchical connections are properly modelled, relying on recent advances in graph theory and Bayesian techniques. This is an exciting area of research that promises to address many of the pitfalls of standard regression methods."

Dr. Marcos Lopez de Prado, Senior Managing Director, GUGGENHEIM PARTNERS, and Research Fellow, LAWRENCE BERKELEY NATIONAL LABORATORY.

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