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- Academic unit or major
- Graduate major in Mathematics
- Instructor(s)
- Ninomiya Syoiti
- Class Format
- Lecture
- Media-enhanced courses
- Day/Period(Room No.)
- Intensive (H201)
- Group
- -
- Course number
- MTH.E440
- Credits
- 2
- Academic year
- 2016
- Offered quarter
- 1Q
- Syllabus updated
- 2016/12/14
- Lecture notes updated
- 2016/4/1
- Language used
- Japanese
- Access Index
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Course description and aims
This course introduces a mathematical model for a probabilistic analysis of the possibility of a creditor (lender of money) incurring financial damage from a debtor (borrower of money) defaulting (not returning money as promised) on their debt (generally referred to as "credit risk"), as well as methods for applying the analysis to the pricing of financial products called credit derivatives such as CDS and bonds with credit risk, and to risk evaluation of the many loan portfolios of banks, etc.
We will also cover counter party risk which is of growing importance for derivatives trading in recent years, starting at the basics and working up to the latest research.
We will also touch on the appeal of the mathematical part of modeling credit risk, but we also wish to present the practical viewpoint of how best to utilize the models in order to accurately explain phenomena observed in actual financial markets,
Student learning outcomes
・See what kind of mathematically difficult problems on credit risk research
・Understand basic ideas and mathematical techniques for both structural and reduced-form approaches, which are typical approaches in mathematical finance
・Understand basic approaches and mathematical techniques for portfolio credit risk modeling
・Understand basic approaches and mathematical techniques for counterparty credit risk modeling
Keywords
credit risk, structural model, hazard rate, corporate bond, CDS, dependence structure of defaults, counterparty credit risk
Competencies that will be developed
| ✔ Specialist skills | Intercultural skills | Communication skills | Critical thinking skills | Practical and/or problem-solving skills |
Class flow
This is a standard lecture course. There will be some assignments.
Course schedule/Required learning
| Course schedule | Required learning | |
|---|---|---|
| Class 1 | Introduction: Mathematical problems on credit risk | Details will be provided during each class |
| Class 2 | Structural models of a default (1) | Details will be provided during each class |
| Class 3 | Structural models of a default (2) | Details will be provided during each class |
| Class 4 | Hazard rate models (1) | Details will be provided during each class |
| Class 5 | Hazard rate models (2) | Details will be provided during each class |
| Class 6 | Extension to hazard rate process models (1) | Details will be provided during each class |
| Class 7 | Extension to hazard rate process models (2) | Details will be provided during each class |
| Class 8 | Models with incomplete information | Details will be provided during each class |
| Class 9 | Portfolio credit risk (1) | Details will be provided during each class |
| Class 10 | Portfolio credit risk (2) | Details will be provided during each class |
| Class 11 | Portfolio credit risk (3) | Details will be provided during each class |
| Class 12 | Portfolio credit risk (4) | Details will be provided during each class |
| Class 13 | Counterparty credit risk | Details will be provided during each class |
| Class 14 | CVA, DVA | Details will be provided during each class |
| Class 15 | Other topics on credit risk modeling | Details will be provided during each class |
Textbook(s)
None required, but not a few topics will be chosen from a few chapters of the reference book below.
Reference books, course materials, etc.
McNeil, Frey, and Embrechts, Quantitative Risk Management: Concepts, Techniques And Tools (revised edition), Princeton (2015)
Assessment criteria and methods
Assignments (100%).
Related courses
- MTH.C361 ： Probability Theory
- MTH.C503 ： Advanced topics in Analysis G
- MTH.C504 ： Advanced topics in Analysis H
Prerequisites (i.e., required knowledge, skills, courses, etc.)
None in particular
