Before modelling default risk mathematically, you need to know what instruments carry it and how practitioners measure credit quality. A loan, a corporate bond, an OTC swap, and a credit default swap (CDS) all embed credit risk — but in different ways and at different layers of complexity. The "default triangle" — exposure at default (EAD), probability of default (PD), and loss given default (LGD) — is the universal decomposition: .
Credit rating migration captures how PD changes over time: firms move between credit quality categories (Aaa through Caa; AAA through C), and this Markov chain description gives a structured way to estimate multi-period default probabilities from single-period transition matrices. This framework is the foundation of the Basel IRB formula and underpins stress testing at banks.
Learning objectives. By the end of this note you should be able to:
- describe loans, bonds, CDS, and OTC derivative counterparty risk as credit-risky instruments;
- define EAD, PD, and LGD and explain the direction of their dependence;
- describe the credit-migration approach: a Markov chain on rating states;
- read off multi-year default probabilities from cumulative default rate tables;
- explain why EAD is stochastic for OTC derivatives and how netting agreements reduce it.
In this lesson
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- The credit-risk universe
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- The default triangle: EAD, PD, LGD
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- Credit quality: ratings and credit scores
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- Credit rating migration as a Markov chain
Before you start
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