Probabilistic graphical models: a new way of thinking in financial modelling Denev, Alexander

Table of contents
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

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).

(http://riskbooks.com/probabilistic-graphical-models-a-new-way-of-thinking-in-financial-modelling)