KTH Matematik  

Matematisk Statistik

Tid: 12 juni 2015 kl 16.15-17.00.

Seminarierummet 3721, Institutionen för matematik, KTH, Lindstedtsvägen 25, plan 7. Karta!

Föredragshållare: Felix Bogren

Titel: Estimation of the term structure of default probabilities for heterogeneous credit portfolios (Master's thesis)

Abstract The aim of this thesis is to estimate the term structure of default probabilities for heterogeneous credit portfolios. The term structure is defined as the cumulative distribution function (CDF) of the time until default. Since the CDF is the complement of the survival function, survival analysis is applied to estimate the term structures. To manage long-term survivors and plateaued survival functions, the data is assumed to follow a parametric as well as a semi-parametric mixture cure model. Due to the general intractability of the maximum likelihood of mixture models, the parameters are estimated by the EM algorithm. A simulation study is conducted to assess the accuracy of the EM algorithm applied to the parametric mixture cure model with data characterized by a low default incidence. The simulation study recognizes difficulties in estimating the parameters when the data is not gathered over a sufficiently long observational window. The estimated term structures are compared to empirical term structures, determined by the Kaplan-Meier estimator. The results indicate a good fit of the model when applied to each credit type separately. Problematically, the validity of the model is difficult to assess when there is a lack of default events. Also, from the results we conclude that the parameter estimation for both models tend to perform poorly with few defaults. The parametric model does however seem less sensitive to low default rates in comparison to the semi-parametric model. In conclusion, the class of mixture cure models are indeed viable for estimating the term structure of default probabilities. Due to the greater flexibility of the model, it is believed to better capture the dynamics of the term structure relative to standard survival analysis.

The full report (pdf)

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Sidansvarig: Filip Lindskog
Uppdaterad: 25/02-2009