Credit Risk

Part 1. of this lecture defines credit risk and places it within the broader context of the economy. Part 2. introduces the main credit risks outcomes and challenges, and Part 3. covers the basic formulas and conventions on the subject.

Part 4. presents the first models of the class: the so-called reduced-form models, which 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 resulting from the default of one of its borrowers.

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

Part 1. introduces the principles of ratings and rating agencies. It also shows how these ratings can be used to assess the probability of default over one year or multiple years for an agent, using transition matrices. Part 2. presents how statistical models can be applied to historical data to score counterparties using logistic regressions. Part 3. is an introduction to credit risk models adapted for modeling climate risks.

Lecture 4 aims to cover portfolio models, which are models used to assess the default risk 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. emphasizes the importance of dependence modeling in these models and introduces copulas for this purpose. Part 3. addresses Asset-Backed Securities (ABS): these 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. Pricing these ABS requires modeling the default of the pooled assets as a whole, necessitating the use of portfolio credit models. To form an ABS, assets are placed in a Special Purpose Vehicle (SPV), which is a company created solely 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 what are known as ABS. The process is called securitization and provides new sources of financing for the aforementioned assets. We then address other derivatives, which do not involve an SPV but have payoffs that depend on a pool of assets, such as Collateralized Synthetic Obligations (CSOs). These provide ways to hedge credit risk for sellers and new investment opportunities for buyers.

Finally, this lecture introduces other synthetic products and hybrids (Part 4.).

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

Naturally, these future losses affect the return on the bank's activities. Models that project future losses are therefore very useful for assessing the profitability of an activity while considering this risk and are thus used to make strategic decisions. Part 2. introduces several tools for this purpose: Risk Adjusted Return On Capital (RAROC), Economic Value Added (EVA), methods for estimating the cost of capital for an activity, and techniques for allocating regulatory capital across various activities.

By selling or buying derivatives, a bank is exposed to the risk of its counterparties defaulting. While such an activity is not a financing activity, it still generates credit risk because the counterparty could default. This risk is referred to as counterparty risk (Part 1.). It differs from the credit risk described earlier in the course for two reasons: first, the amount involved depends on market data, and second, the risk is symmetric (both the seller and the buyer may fear the default of their respective counterparties). 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 new regulations on the matter and (ii) price this risk and account for it when selling derivatives (e.g., Expected Effective Positive Exposure - EEPE, Credit Valuation Adjustment - CVA). Part 3. introduces other Valuation Adjustments (e.g., FVA, KVA, IMVA).

The goal of this case study is to help students understand what triggered the subprime mortgage crisis and the role played by 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 experience the events that occurred from 2006 (the boom of CDOs) to 2008 (the height of the crisis) while playing their respective roles.

Traders and structurers will protect their interests and those of their clients; the rating agency will follow its defined rating processes; the risk department will defend the interests of its bank; the CVA desk and investors will seek returns.

Pricing tools, market condition data, instructions, and deadlines will be provided to participants throughout the case study.

At the end of the simulation, the realized losses incurred by each agent will be calculated.

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.

2024-2025 projects will be published on the website at the end of october.