Change search
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf
Estimating the Term Structure of Default Probabilities for Heterogeneous Credit Porfolios
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
2015 (English)Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesisAlternative title
Estimering av terminstrukturen för konkurssannolikheter i heterogena kreditportföljer (Swedish)
Abstract [en]

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 indicated a good fit of the model for longer horizons when applied to each credit type separately, despite difficulties capturing the dynamics of the term structure for the first one to two years. Both models performed poorly with few defaults. The parametric model did however not seem sensitive to low default rates. In conclusion, the class of mixture cure models are indeed viable for estimating the term structure of default probabilities for heterogeneous credit portfolios.

Abstract [sv]

Syftet med den här uppsatsen är att estimera terminstrukturen för konkurssannolikheter i heterogena kreditportföljer. Terminstrukturen definieras som den kumulativa fördelningsfunktionen för tiden till konkurs. Eftersom den kumulativa fördelningsfunktionen är komplementet till överlevnadsfunktionen kan överlevnadsanalys appliceras för att estimera terminstrukturen.  För att hantera långtidsöverlevare samt överlevnadsfunktioner som planar ut vid nivåer över noll, antar vi att observationerna kommer från en parametrisk såväl som en semiparametrisk mixture cure model. På grund av numeriska svårigheter att hantera maximum likelihood-funktionen för mixture modeller, så skattas parametrarna med hjälp av EM algoritmen. En simulationsstudie genomfördes för att undersöka precisionen av EM algoritmen applicerad på parametriska specifikationen av modellen, med data bestående av få antal konkurser. Simulationsstudien påvisade svårigheter att estimera parametrarna när urvalet inte tagits från en tillräckligt lång tidsperiod. En jämförelse görs med de empiriska terminstrukturerna, framtagna med Kaplan-Meier's skattning av överlevnadsfunktioner. Resultaten påvisar en bra anpassning när modellen appliceras på varje kredittyp separat, trots svårigheter att fånga dynamiken de av terminstrukturen under

Place, publisher, year, edition, pages
2015.
Series
TRITA-MAT-E, 2015:39
National Category
Probability Theory and Statistics
Identifiers
URN: urn:nbn:se:kth:diva-169455OAI: oai:DiVA.org:kth-169455DiVA: diva2:821274
External cooperation
Swedbank
Subject / course
Mathematical Statistics
Educational program
Master of Science - Industrial Engineering and Management
Supervisors
Examiners
Available from: 2015-06-15 Created: 2015-06-15 Last updated: 2015-06-15Bibliographically approved

Open Access in DiVA

fulltext(10574 kB)149 downloads
File information
File name FULLTEXT01.pdfFile size 10574 kBChecksum SHA-512
e054b157bdba1784201c1ed5fbb63c25887a2b907a2a466495572bd444f022f1b3da450aa29de6448c2f697ac146c7e95b7169cabe9b69975dde344562868aa3
Type fulltextMimetype application/pdf

By organisation
Mathematical Statistics
Probability Theory and Statistics

Search outside of DiVA

GoogleGoogle Scholar
Total: 149 downloads
The number of downloads is the sum of all downloads of full texts. It may include eg previous versions that are now no longer available

urn-nbn

Altmetric score

urn-nbn
Total: 194 hits
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf