F71CM Credit Risk Modelling
Lecturer: Alexander McNeil
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
- Calibration and statistical inference for credit risk models
- Introduction to credit derivatives
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 and apply statistical approaches to calibrating credit risk models.
- Describe the cash flows of common single-name and basket credit derivatives and have some idea of how they are valued.
Reading
- McNeil, A.J. and Frey, R. and Embrechts, P. (2005). Quantitative Risk Management: Concepts, Techniques and Tools. Princeton, New Jersey.
- Bluhm, C. and Overbeck, L. and Wagner, C. (2002). An Introduction to Credit Risk Modeling. Chapman & Hall/CRC Financial Mathematics Series, London.
Assessment
There will be a two-hour examination carrying at least 70% of the credit and coursework carrying up to 30% of the credit.
Help
If you have any problems or questions regarding the course,
you are encouraged to
contact the lecturer.
Material online
Further information and course materials are available at
Heriot-Watt VISION
Detailed syllabus
- Introduction to Credit Risk: credit-risky instruments, the
nature of the challenge, defaults, exposures, losses given default, a
first look at default dependence
- Merton's Model: the relationship between asset value, debt and equity, pricing in Merton's model
- Industrial Implementations of Merton's Model: KMV and CreditMetrics
- Latent Variable or Threshold Models: a short copula primer, role of copulas in threshold models, industry models as threshold models
- Mixture Models: exchangeable models, one-factor models, mapping threshold models to mixture models, CreditRisk+
- The Portfolio Loss Distribution: calculating the portfolio
los distribution, Monte Carlo methods, asymptotic results in infinitely
granular portfolios, the Basel II regulatory formula
- Statistical Estimation: estimating default probabilities and default correlation; relationship to generalized linear mixed models (GLMMs)
- Introduction to Credit Derivatives: the credit default swap (CDS); the collateralized debt obligation (CDO)
