MC_finance - IEOR 4106 Introduction to OR Stochastic Models...

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IEOR 4106: Introduction to OR: Stochastic Models Spring 2009, Professor Whitt A Markov Chain Example in Credit Risk Modelling This is a concrete example of a Markov chain from finance. Specifically, this come from p.626- 627 of Hull’s Options, Futures, and Other Derivatives , 5th edition. This is not a homework assignment. Questions are posed, but nothing is required. Background. Over time, bonds are liable to move from one rating category to another. This is sometimes referred to as credit ratings migration . Rating agencies produce from historical data a ratings transition matrix . This matrix show the probabiltiy of a bond moving from one rating to another during a certain period of time. Usually the period of time is one year. Below is a table giving a rating transition matrix produced from historical data by Standard and Poor’s (S&P). Table 1: One-year transition probabilities matrix. Initial Ratings at year-end ratings AAA AA A BBB BB B CCC Default AAA 0.9366 0.0583 0.0040 0.0009 0.0002 0 0 0 AA 0.0066 0.9172 0.0694 0.0049 0.0006 0.0009 0.0002 0.0002 A 0.0007 0.0225 0.9176 0.0518 0.0049 0.0020 0.0001 0.0004 BBB 0.0003 0.0026 0.0483 0.8924 0.0444 0.0081
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