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NJIT Academic Integrity CODE:  All Students should be aware that the Department of Mathematical Sciences takes the University Code on Academic Integrity at NJIT very seriously and enforces it strictly.  This means that there must not be any forms of plagiarism, i.e., copying of homework, class projects, or lab assignments, or any form of cheating in quizzes and exams.  Under the University Code on Academic Integrity, students are obligated to report any such activities to the Instructor.

 

 

Number of Credits:  3

 

Course Description:  This course explores mathematical models and methods for credit risk measurement and rating. The nature of credit risk is reviewed through examination of credit instruments, including credit default swaps, collateralized debt obligations, and basket credit derivatives. These instruments, through which risk exposure opportunities and hedging possibilities are created and managed, are explored with respect to dynamics and valuation techniques, applying PDE methods and stochastic processes. Effective From: Fall 2011

Prerequisites:  Prerequisites: Math 604, 605, 606 or permission of the instructor.

Textbook:  Credit Derivatives Pricing Models: Models, Pricing and Implimentation by Philipp Schonbucher; ISBN-13: 978-0-470-84291-1

Companion text: Credit Risk Modeling using Excel and VBA, by Gunter Loffler and Peter N. Posch

 

More textbooks on credit risk analysis

 

1. Credit Risk: Theory and Applications, by David Lando

2. Credit Risk Models; Valuation and Hedging, by Thomasz Bielecki

3. Credit Risk, by Darrell Duffie and Kenneth J. Singleton

4. Modelling Single-name and Multi-name Credit Derivatives, by Dominic O’Kane

5. Introduction to Credit Risk Modeling, by Christian Bluhm, Ludger Overbeck, and Christoph Wagner

Introductory and background material can also be found in the following:

 

• Options, Futures, and Other Derivatives, by John C. Hull – in the 7^th edition the relevant chapters are chapter 22 Credit Risk and chapter 23 Credit Derivatives;

• Fixed Income Analysis, by Frank J. Fabozzi – 2^nd edition, chapter 15 General Principles of Credit Risk Analysis, chapter 20 Relative Value Methodologies for Global Credit-Bond Portfolio Management, chapter 24 Credit Derivatives in Bond Portfolio Management.

• The risk management perspective is the focus of Risk Management by Michel Crouhy, Dan Galai, and Robert Mark.

Instructor:   (for specific course-related information, follow the link below)

 

Math 607-101

Prof. Pole

 

 

 

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MATH DEPARTMENT CLASS POLICIES LINK 

All DMS students must familiarize themselves with and adhere to the Department of Mathematical Sciences Course Policies, in addition to official university-wide policies. DMS takes these policies very seriously and enforces them strictly. For DMS Course Policies, please click here.

September 3, 2012	M	Labor Day ~ No classes
November 6, 2012	T	Last Day to Withdraw from this course
November 20, 2012	T	Classes follow a Thursday Schedule
November 21, 2012	W	Classes follow a Friday Schedule
November 22-25, 2012	R-Su	Thanksgiving Recess
December 13, 2012	R	Reading Day
December  14-20, 2012	F- R	Final Exams

 

Course Outline:

 

Week 1:  Introduction

Types of credit risk; overview of credit instruments

Asset swaps, total return swaps, credit default swaps

Credit spread products, credit linked notes;

 

Week 2:  Credit Derivatives

Hedge based pricing

Default correlation products and CDOs

 

Week 3:  Credit Spreads & Bond Price Based Pricing

Implied default probabilities

Recovery modeling

Pricing

 

Week 4:  Credit Spreads & Bond Price Based Pricing

Constructing and calibrating credit spread curves

 

Week 5:  Intensity Models (Reduced Form)

Poisson processes & spreads

Inhomogeneous Poisson processes

 

Week 6:  Intensity Models (Reduced Form)

Stochastic credit spreads

Cox processes, compound Poisson processes

 

Week 7:  Intensity Based Models: Recovery Modeling

Zero recovery, recovery of treasury, recovery of par

Multiple defaults, recovery of market value

Stochastic recovery

 

Week 8:  MID TERM EXAM

 

Week 9:  Intensity Based Models

Two factor and multifactor Gaussian models, multifactor CIR model

Implied survival probabilities

Default payoffs

 

Week 10:  Intensity Based Models: implementation

Tree models

PDE implementation

Monte Carlo simulation

 

Week 11:  Credit Rating Models

Rating process and transition probabilities

Logistic regression

Estimation, calibration and pricing

 

 

Week 12:  Structural Models

Merton’s model

First Passage

KMV and CreditGrades models

 

Week 13:  Default Correlation

Factor models

Correlated intensity models

Copulas

 

Week 14:  Default Correlation

Risk analysis

Pricing structured credit: CDOs and first-to-default

 

Week 15:  FINAL EXAM

 

Prepared By:  Prof. Andrew Pole

Last revised: May 2, 2012