Mathematics 16:643:624 Credit Risk Modeling


The course is offered during the Fall semester.
  • Class meeting dates: Please visit the University's academic calendar.
  • Schedule and Instructor: Please visit the University's schedule of classes for the instructor, time, and room.
  • Instructor and Teaching Assistant Office Hours: Please visit the Mathematical Finance program's office hour schedule.

Course Abstract

In addition to equity, interest rates, FX, and commodity derivatives, credit derivatives play an increasingly important role in financial markets. The course will include a review of jump processes; the basic theory of single name credit derivative modeling; structual, reduced form or intensity models; credit default swaps; default correlation, multiname credit derivative modeling; top down versus bottom up models; basket credit derivatives; collaterized debt obligations; and tranche options. The goal of the course is to cover most of the material in "Credit Risk Modeling" by David Lando (Princeton University Press, 2004) or "CrediT Derivatives Pricing Models" by Philipp Schonbucher (Wiley, 2004).


Math 16:643:621 (Mathematical Finance I) and Math 16:643:573 (Numerical Analysis I)


Math 16:643:622 (Mathematical Finance II).

Required Textbooks

  • (OK) D. O'Kane, Modeling Single-Name and Multi-Name Credit Derivatives , Wiley, 2008


All course content – lecture notes, homework assignments and solutions, exam solutions, supplementary articles, and computer programs – are posted on Sakai and available to registered students.


The recommended grading scheme, subject to instructor confirmation, is: Class attendance 5%, homework 15%, midterm exam 30%, quiz 10%, and final project 40%. Exams and quizzes are in-class.

Class Policies

Please see the MSMF common class policies.

Weekly Lecturing Agenda and Readings

This page will record the topics we cover in each week, reading assignments, and additional information as needed. Reading material from the texts on the reserve list is strongly suggested, but not absolutely necessary. Reading material from the class text and handouts is required. Students should study the reading assignments before class.
WeekTopicsReading Assignments
1 Credit Derivatives: definitions, markets, main credit derivatives B, ch. 1,2, 3, OK, ch. 1
2 Defaultable bonds, credit curves, credit default swaps, risk-neutral valuation OK, ch. 4,5,6
3 Structural models OK, ch.3, B, ch. 17.1, S, ch.9
4 Reduced-form approach OK, ch.3, B, ch. 17.2, S, ch.5
5 Credit rating models S. ch.8
6 CDS risk management. Advanced credit derivatives OK, ch.8, 9
7 Credit default swaptions OK, ch.9
Mid-term exam
8 Introduction to portfolio credit derivatives OK, ch.10,12
9 The CreditMetrics/Vasicek model OK, ch.13,16
10 Methods of calculation of loss distributions. Introduction to copulae OK, ch.18 and 14
11 Implied correlations and base correlations OK, ch. 19,20
12 Skew models for credit portfolios (RFL, loss surface, implied copula) OK, ch. 21
13 Copula skew models. Pricing default baskets OK, ch. 21, 15
14 Risk management of tranches. Advanced multi-name credit derivatives OK, ch. 17, 22
15 Dynamic credit portfolio models (bottom-up and top-down) OK, ch. 23, 24
16 Final exam  

Library Reserves

All textbooks referenced on this page should be on reserve in the Hill Center Mathematical Sciences Library (1st floor). Please contact the instructor if reserve copies are insufficient or unavailable.

Additional Textbooks

Class lectures will draw on material from the following texts and current research articles. Please see the Rutgers Mathematical Finance Reference Texts blog for additional textbooks.
  • (DS) D. Duffie and K. Singleton, Credit Risk, Princeton University Press, 2003
  • (B) A.N. Bomfim, Understanding Credit Derivatives and Related Instruments, Elsevier, 2005
  • (S) P. Schonbucher, Credit Derivatives Pricing Models, Wiley, 2003