Credit Risk - ENPC

# Credit Risk

## École Nationale des Ponts et Chaussées

Département Ingénieurie Mathématique et Informatique (IMI) – Master II

This course is part of the training cycle of École Nationale des Ponts et Chaussées: it is a Master II course from the Département Ingénieurie Mathématique et Informatique (IMI).

Its goal is to provide students with an applied and extensive understanding of what credit risk is, through the presentation of credit models, their use by financial institutions and their importance in the economy as a whole. The course starts by presenting theoretically the models, and then, applies them on concrete examples and real data.

Lessons are organized so as to cover three main aspects:

• Give an overview of the banking environment focusing on challenges entailed by credit risk, among other by exploring their links with the subprime mortgage crisis (2007-2009) and the current regulatory reforms (Basel III, IFRS9, etc.);
• Have the students become familiar with most classical credit instruments (bonds, Credit Default Swap, Asset-Backed Securities, Collateralized Synthetic Obligation, etc.): understanding their use, measuring their associated risks and being able to price them (modeling techniques, simulations, stress testing);
• Prepare the students to their next professional life, giving them the opportunity to conduct a R&D project on current topics, and experiencing the challenges faced by quant teams through the subprime mortgage crisis during a three-hour case study.

The lessons take place from October to December. They are validated after a written exam, participation during classes, and a project presentation. The lecture slides, exercises and their correction are available in the "Syllabus" part of the course website.

Access to the Credit Risk Cheat Sheet
Lecture 1 – Reduced-form models and Credit Default Swaps (CDS)
Date: 04/10/2019
Teacher: François CRENIN
Abstract

Part 1. presents the structure and the assignments of the class. Part 2. defines credit risk and places it in the wider frame of the economy. Part 3. introduces the main credit risks outcomes and challenges, and Part 4. the basic formulas and conventions on the subject.

Part 5. presents the first models of the class: the so-called reduced-form models that are part of the single-name models (with rating models – Lecture 2 – and structural models – Lecture 3) designed to model the default of only one agent. Part 6. introduces Credit Default Swaps: CDS are contracts that protect the buyer from losses consequent to the default of one of its borrowers.

Table of contents:
1. Class structure and assignments
2. Credit risk management is at the base of our economies
3. Main credit risk outcomes and challenges
4. The basics of credit risk
5. Reduced-form models
6. Single-name credit derivatives and Credit Default Swaps (CDS)
Lecture 2 – Statistical models
Date: 11/10/2019
Teacher: François CRENIN
Abstract

Part 1. introduces the principle of ratings and the rating agencies. Part 2. shows how these ratings can be used to assess the probability of default on one year, or several years, of an agent, using transition matrices. Part 3. presents how statistical models use historical data to score counterparties (scoring with logistic regressions and new data science techniques).

Table of contents:
1. Default and Ratings
2. The rating-based models
3. Statistical approached to rate counterparties
Lecture 3 – Structural models: Merton and Leland models
Date: 18/10/2019
Teacher: Loïc BRIN
Abstract

Part 1. introduces the structural models: based on the modeling of the balance sheets of the agent, they were the first created (before reduced-form and rating models), and provide precious economic and corporate finance insights. Part 2. presents the first structural model, the Merton model, that is based on the diffusion of the equity of a firm through the time, and consider a default as soon as the value of the equity is lower than zero at the maturity of the considered debt. Part 3. goes through the Leland model that proposes an interesting alternative to Merton's model by addressing some of its limits.

Table of contents:
1. Introduction to structural models
2. The Merton model
3. The Leland model
Lecture 4 – Portfolio Models and Asset Backed Securities (ABS, CDO, CSO, etc.)
Date: 25/10/2019
Teacher: Benoît ROGER
Abstract

Lecture 4 aims at covering portfolio models, that is models used to assess the default of a portfolio of debts, and then apply these to price Asset Backed Securities (ABS).

Part 1. presents the most popular portfolio model: the Vasicek model. Part 2. stresses on the importance of dependence modeling in these models, and introduces copulas for the matter. Part 3. deals with Asset-Backed Securities (ABS): they are securities whose cash flows (and thus prices) depend on the cash flows generated by a pool of assets such as home loans, auto loans, student loans, bonds, etc. In all the cases, pricing these ABS requires the modeling of the pool assets default as a whole and thus the use of portfolio credit models. To form an ABS, assets are placed in a Special Purpose Vehicle (SPV), that is, in a company whose only purpose is to hold assets and redistribute the cash flows generated by these assets: this company is financed through equity and bonds and these equities and bonds are the so-called ABS. The above process is called securitization and provides new sources of financing for the above-mentioned assets. We then tackle the case of other derivatives, with no SPV, that have payoffs that depend on a pool of assets too, as Collateralize Synthetic Obligations; they provide ways to hedge credit risk for the sellers and new kind of investment for the buyers.

Eventually, this lecture will introduce other synthetic products and hybrids (Part 4.).

Table of contents:

1. The Vasicek model, a one factor portfolio model
2. Modeling dependence structure with copulas
3. Collateralized Debt Obligation (CDO) and Collateralized Synthetic Obligation (CSO)
4. Other synthetic products and hybrids
Lecture 5 – Risk Modeling and Bank Steering
Date: 08/11/2019
Teacher: Benoît ROGER
Abstract

Credit risk models are not only used for commercial purpose (pricing contracts); they are also used by top managers to steer the bank (Part 1.) as they are used to measure the amount of provisions (amounts of money dedicated to cover expected future losses), to evaluate the required capital to face the above-expectation losses (economic capital), and to fulfill regulatory requirements (regulatory capital).

Of course, these future losses alter the return of the activities of the bank. Models, by projecting future losses, are thus very useful to assess the profitability of an activity taking this risk into account, and are thus used to make strategic decisions. Part 2. presents several tools to do so: the Risk Adjusted Return On Capital (RAROC), the Economic Value Added (EVA), how to estimate the cost of capital of an activity, and how to distribute regulatory capital induced by several activities among them.

Table of contents:
1. Credit risk models to fulfill regulatory requirements and prevent the bank from failure
2. Reevaluating activities' profitability taking credit risk into account
Lecture 6 – Counterpaty risk (EEPE, CVA, WWR, etc.)
Date: 15/11/2019
Teacher: Loïc BRIN
Abstract

By selling or buying derivatives, a bank is exposed to the risk of default of its counterparties. Such an activity is not a financing activity but is yet the source of credit risk as the counterparty could default: this risk is thus called the counterparty risk (Part 1.). It differs from the credit risk that was described until now in the class for two reasons: first the amount involved depends on market data, second, the risk is symmetric (both the seller and the buyer may fear the default of their respective counterparty).

Part 2. shows that counterparty risk metrics are used to (i) monitor counterparty risk within the bank and comply with the new regulation on the matter (Expected Effective Positive Exposure - EEPE) and (ii) to price this risk and take it into account when selling derivatives (Counterparty Value Adjustment - CVA). Part 3. introduces the concept of Wrong-Way Risks (WWR) and Right-Way Risks (RWR) in the light of CVA and DVA. Part 4. covers different techniques that can be used to mitigate this risk, such as the use of netting contracts and clearing houses.

Table of contents:
1. Counterparty risk - Introduction
2. Counterparty risk metrics
3. Wrong Way Risks and Right Way Risks
4. Counterparty risk mitigations
Lecture 7 – Case Study: the Subprime Mortgage Crisis
Date: 29/11/2019
Teacher: Loïc BRIN & François CRENIN
Abstract

This case study's intention is to make students understand what triggered the subprime mortgage crisis and what role played the different agents involved. Seven agents (a rating agency, a Negative Basis Trade (NBT) desk of a bank, the risk department, CDO of RMBS structurers, the CVA desk of the same bank, and investors) will live the events that occurred from 2006 (booming of the CDOs) to 2008 (the heart of the crisis) playing their respective roles.

Traders and structurers protect their interests and the one of their clients; the rating agency respects its defined rating processes; the department of risk defends the interests of its bank; the CVA desk and investors look for return.

Pricing tools, data on market conditions, instructions and deadlines will be handed to the participants all along the case study.

At the end of the game, realized losses by each agent will be computed.

Exam – Exam and Q&A on the Project
Date: 06/12/2019
Teacher: Loïc BRIN & François CRENIN
Abstract

The exam lasts for one hour and a half, and is made of three exercises.

The last hour of the lecture is devoted to the projects through round tables: the teachers drive the group in their projects by answering their questions.

Structure of the exam:

1. A technical exercise of mathematical finance (for instance a pricing question)
2. An exercise of finance (for instance solving a hedging issue)
3. A non-technical question (for instance answering a question about credit risk within our economies)
Projects
Date: 06/12/2019
Teacher: Loïc BRIN & François CRENIN & Benoît ROGER
Abstract

Students gathered in groups of 2 or 3 must conduct a project to pass the class. These projects are based on recent published papers and consist in studying the existing bibliography on the subject, and implementing numerically the paper focusing on the methodological choices that were made.

Students must write a small report (maximum 15 pages) and make available their code that will be tested with the teachers during an oral presentation.

2019-2020 projects will be published on the website at the end of october.

List of 2019-2020 projects:
1. Infectious defaults
2. Predict bankruptcies of Polish companies
3. Securitization and bank steering

Loïc BRIN worked in the risk modeling team of Société Générale and is now part of the General Inspection of the same bank (strategic audit and consulting assignments related to all Group activities in France and abroad on behalf of Societe Générale Top Management). He graduated from HEC Paris, ENSAE ParisTech in statistics and economics, Paris 7 with a Master of Research in stochastic calculus (ex-DEA Laure Élie) and from the Institute of French Actuaries. His current research projects are in the area of applications of random matrix theory in risk measurement.

François CRENIN is is Quantitative project manager of Operational Risk Modeling at Société Générale. François joined the Operational risk modeling team in 2013, after several experiences in the banking industry and consulting. He has been working on various statistical issues of the Operational risk measurement with a focus on dependence structure. He graduated from ESSEC Business School, ENSAE as a Statistician and Economist and from the Institute of French Actuaries.

Benoît ROGER is since september 2019 mission Director on Data and Artificial Intelligence for EURO Business Line of Société Générale. Prior turning back to Paris, Benoit was Chief Representative at BDK (Bank Deutsches Kraftfahrzeuggewerbe), the German Car Financing affiliate of Societe Générale. In his previous experiences, Benoit has been Head of Retail Risk for International Banking and Financial Services and Deputy Head of Transversal Risk Monitoring. Benoît is a former student of Ecole Normale Supérieure de Lyon, in Mathematics and first started teaching at Ecole des Ponts in 2005. Benoît has published one book on credit risk with Vivien Brunel: "Le risque de crédit : des modèles au pilotage" (Ed. Economica).

Final Grade Formula
The final grade will be computed with this formula:

$$\mathsf{\text{Final Grade}=\frac{\text{Class participation}+\text{Final Exam}+\text{Project}}{3}}$$

With:

\begin{eqnarray} \mathsf{\text{Class Participation}} & = & \mathsf{\underbrace{\text{Participation during the case study}}_{\text{grade over 10}}}\\&+&\mathsf{\underbrace{\text{Participation during class tutorials}}_{\text{grade over 10}}} \\[3em] \mathsf{\text{Final Exam}} & =&\mathsf{\underbrace{\text{Technical Exercise}}_{\text{grade over 8}}}\\&+&\mathsf{\underbrace{\text{Finance Exercise}}_{\text{grade over 6}}}\\&+&\mathsf{\underbrace{\text{A non technical question}}_{\text{grade over 6}}}\\[3em] \mathsf{\text{Project}}&=&\mathsf{\underbrace{\text{The report}}_{\text{grade over 12}}}\\&+&\mathsf{\underbrace{\text{The oral presentation}}_{\text{grade over 8}}} \end{eqnarray}

The purpose of this infography is to understand the links between the different notions covered by this class.