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Estimating Probability of Default Using Rating Migrations in Discrete and Continuous Time
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
2014 (English)Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
Abstract [en]

During the financial crisis that began in 2008, even whole countries and very large companies defaulted or were on the verge of defaulting. The turmoil made risk managers and regulators more vigilant in scrutinising their risk assessment. The probability of default (PD) is an essential parameter in measuring counterparty credit risk, which in turn has impact on pricing of loans and derivatives. The last decade, a method using Markov chains to estimate rating migrations, migration matrices and PD has evolved to become an industry standard. In this thesis, a holistic approach to implementing this approach in discrete and continuous time is taken. The results show that an implementation in continuous time has many advantages. Also, it is indicated that a bootstrap method is preferred to calculate confidence intervals for the PDs. Moreover, an investigation show that the frequently used assumption of time-homogeneous migration matrices is most probably wrong. By studying expansions and recessions, specific expansion and recession migration matrices are calculated to mitigate the impact of time-inhomogeneity. The results indicate large differences of estimated PDs over the economic cycle, which is important knowledge to be able to quote correct prices for financial transactions involving counterparty credit risk.

Place, publisher, year, edition, pages
TRITA-MAT-E, 2014:49
National Category
Mathematical Analysis
URN: urn:nbn:se:kth:diva-150428OAI: diva2:747996
Subject / course
Mathematical Statistics
Educational program
Master of Science - Mathematics
Available from: 2014-09-17 Created: 2014-09-04 Last updated: 2014-09-17Bibliographically approved

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