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:
The lessons take place from October to December. We evaluate students through a written exam, participation during classes, and their credit risk project. The lecture slides, exercises and their correction are available in the "Syllabus" part of the course website.
Part 1. of this lecture defines credit risk and places it in the wider frame of the economy. Part 2. introduces the main credit risks outcomes and challenges, and Part 3. the basic formulas and conventions on the subject.
Part 4. 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 5. introduces Credit Default Swaps: CDS are contracts that protect the buyer from losses consequent to the default of one of its borrowers.
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.
Part 1. introduces the principle of ratings and the rating agencies. It also 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 2. presents how statistical models can be used on historical data to score counterparties, using logistic regressions. Part 3. is an introduction to credit risk models adapted to model climate risks.
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 introduces other synthetic products and hybrids (Part 4.).
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.
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).
This part also covers different techniques that can be used to mitigate this risk, such as the use of netting contracts and clearing houses.
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 and (ii) to price this risk and take it into account when selling derivatives (e.g.Expected Effective Positive Exposure - EEPE, Counterparty Value Adjustment - CVA).
Part 3. introduces other Valuations Adjustments (e.g. FVA, KVA, IMVA).
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.
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.
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.
2023-2024 projects will be published on the website at the end of october.
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.
Benoît ROGER is since April 2020 Principal at Ares and Co., a strategy consulting firm based in Paris dedicated to Banks, Insurances and Funds. Prior joining Ares and Co., Benoit was Chief Representative at BDK (Bank Deutsches Kraftfahrzeuggewerbe), the German Car Financing affiliate of Societe Générale and for a few months mission Director on Data and Artificial Intelligence for EURO Business Line of Société 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).
The purpose of this infography is to understand the links between the different notions covered by this class.