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# Credit Risk (Online Version) - MAT00085M

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• Department: Mathematics
• Credit value: 20 credits
• Credit level: M
• Academic year of delivery: 2024-25

## Module summary

Teaching Cycle : One (for fast stream students) or two (for standard stream students) consecutive four-month online teaching periods: 1 October to 31 January and/or 15 March to 15 July; two starting dates per annum (1 October, 15 March).

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## Module will run

Occurrence Teaching period
A1 Semester 1 2024-25
A2 Semester 1 2024-25 to Semester 2 2024-25
B1 Semester 2 2024-25
B2 Semester 2 2024-25 to Summer Semester 2024-25

## Module aims

The module enables students to acquire in-depth knowledge of the main features and models of credit risk, including:

- Defaultable securities: defaultable bonds and their recovery schemes, CDS (credit default swaps), general zero-recovery and positive-recovery securities;

- Reduced-form credit risk models (the hazard function and hazard process models) and conditions for the absence of arbitrage in these models;

- Information flow and filtrations in reduced-form models;

- Martingale properties and martingale representation in reduced-form models as applied to pricing and hedging defaultable securities;

- Structural modelling of debt on the basis of company values, under default conditions.

## Module learning outcomes

By the end of this module students should

1. Be able to identify basic defaultable securities and their features.
2. Demonstrate fluency in handling the mathematical tools (filtrations, conditional expectation with respect to such filtrations, martingale properties) involved in the hazard function model if credit risk.
3. Be able to construct hedging strategies and to price defaultable securities within the hazard function model.
4. Demonstrate fluency in handling the mathematical tools (filtrations and their extensions, conditional expectation with respect to such filtrations, martingale properties) involved in the hazard process models if credit risk.
5. Be able to construct hedging strategies and to price defaultable securities within the hazard process model.

Be familiar with tenets of the Merton structural model and the barrier model of credit risk and able to deploy these models in company valuation under conditions of default.

## Module content

Indicative Content:

1. Hazard function model and the absence of arbitrage.
2. Security pricing and replication in the hazard function model.
3. Hazard process model.
4. Canonical construction of default time.
5. Security pricing with hazard process.
6. Structural models of credit risk.

## Indicative assessment

Coursework - extensions not feasible/practicable 100
Oral presentation/seminar/exam 0

None

### Indicative reassessment

Coursework - extensions not feasible/practicable 100
Oral presentation/seminar/exam 0

## Module feedback

Current Department policy on feedback is available in the student handbook. Coursework and examinations will be marked and returned in accordance with this policy.