# F71CM Credit Risk Modelling

Course co-ordinator(s): Dr Jing Yao (Edinburgh).

Aims:

This course aims to introduce students to the models used in the management of portfolio credit risk. We explore the mathematical underpinnings of widely-used industry models, such as the Moody’s KMV model, CreditMetrics and CreditRisk+, and learn how the critical phenomenon of default dependence is modelled. We show how these portfolio credit models are used to determine capital adequacy and reveal how they have shaped regulation and led to the Basel II capital formula.There will also be a short introduction to credit derivatives.

Summary:

In this course we will cover the following topics:

• Introduction to credit risk: credit-risky instruments, defaults, ratings
• Merton’s model of the default of a firm
• Common industry models (KMV, CreditMetrics, CreditRisk+)
• Modelling dependence between defaults with factor models
• Latent variable or threshold models of default
• Mixture models of default
• The Basel II regulatory capital formula
• Calculating the portfolio credit loss distribution
• Large portfolio behaviour of the credit loss distribution
• Introduction to credit derivatives

## Detailed Information

Pre-requisites: none.

Location: Edinburgh.

Semester: 2.

Syllabus:

1. Introduction to Credit Risk: credit-risky instruments, the nature of the challenge, defaults, exposures, losses given default, a first look at default dependence
2. Merton’s Model: the relationship between asset value, debt and equity, pricing in Merton’s model
3. Industrial Implementations of Merton’s Model: KMV and CreditMetrics
4. Latent Variable or Threshold Models: a short copula primer, role of copulas in threshold models, industry models as threshold models
5. Mixture Models: exchangeable models, one-factor models, mapping threshold models to mixture models, CreditRisk+
6. The Portfolio Loss Distribution: calculating the portfolio los distribution, Monte Carlo methods, asymptotic results in infinitely granular portfolios, the Basel II regulatory formula
7. Introduction to Credit Derivatives: the credit default swap (CDS); the collateralized debt obligation (CDO)

Learning Outcomes:

On completion of the course the student should be able to:

• Demonstrate an understanding of the nature of credit risk;
• Describe the theoretical underpinnings of models used in the financial industry;
• Show a knowledge of the regulatory framework and, in particular, the Basel II regulatory capital formula;
• Explain how dependence is modelled in credit portfolios;
• Explain how latent variable or threshold models are constructed;
• Describe mixture models of default and derive their mathematical properties;
• Describe methods for calculating the portfolio loss distribution, including asymptotic approximations;
• Describe the cash flows of common single-name and basket credit derivatives and have some idea of how they are valued.