### 2016　Special lectures on advanced topics in Mathematics Q

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Instructor(s)
Ninomiya Syoiti
Course component(s)
Lecture
Mode of instruction

Day/Period(Room No.)
Intensive (H201)
Group
-
Course number
MTH.E440
Credits
2
2016
Offered quarter
1Q
Syllabus updated
2016/12/14
Lecture notes updated
2016/4/1
Language used
Japanese
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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