Department of Mathematics

MAL843 Mathematical Modelling of Credit Risk

3 credits (3-0-0)

 

 

Pre-requisite

1.      MTL106 or MAL250 or MAL509, and

2.      MAL732, and

3.      MAL733 or MAL725 or MEL770

 

Course Contents

1.      Introduction to credit risk

1.1    Credit risk

1.1.1        Historical and risk neutral probabilities

1.1.2        Bond prices and default probability

1.2    Credit risk modelling

1.3    Credit derivatives

1.4    Modelling assumptions

1.4.1        Probability space and filtrations

1.4.2        The risk free asset

 

2.      Single-name credit derivatives

2.1    Credit default swaps

2.1.1        Credit default swaps pricing

2.1.2        Calibration assumptions

2.2    Credit default swaps forward

2.2.1        Credit default swaps pricing

2.3    Constant maturity credit default swaps

2.3.1        Constant maturity credit default swaps pricing

2.4    Options on CDS

 

3.      Collateralized debt obligations

3.1    Gaussian one factor model

3.2    Generic one factor Levy model

3.3    Examples of Levy models

 

4.      Statistical techniques of analyzing defaults

4.1    Credit scoring with Logistic regression

4.2    Credit scoring with discriminant analysis

4.3    Hazard regression: Discrete case

4.4    Continuous time survival analysis method

4.5    Markov chains and transition probability estimation

 

5.      Credit Scoring models

5.1    Credit scoring and internal rating

5.2    Construction of credit scoring models

5.3    Logistic regression

5.4    Fisher’s linear discriminant analysis

 

6.      Firm-value Levy models

6.1    The Merton model

6.2    The Black-Cox model with constant barrier

6.3    The Levy-first passage model

6.4    The variance-gamma model

 

7.      Intensity Levy models

7.1    Intensity models for credit risk

7.1.1        Jarrow-Turnbull model

7.1.2        Cox models

7.2    The intensity-OU model

7.3    Calibration of models on CDS term structure

 

Text Books

1.      Wim Schoutens and Jessica Cariboni, ``Levy processes in credit risk”, John Wiley, 2009.

2.      David Lando, ``Credit risk modelling- Theory and applications”,New age international publisher, 2005.

3.      Suresh Chandra, S. Dharmaraja, Aparna Mehra, Reshma Khemchandani, ``Financial mathematics-An introduction”, Narosa Publisher, 2013.

 

This page maintained by Dr. S. Dharmaraja mailto:dharmar@maths.iitd.ac.in and last updated Wednesday, May 18, 2016.