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On the Multidimensional Default Threshold Model for Credit Risk

Title: On the Multidimensional Default Threshold Model for Credit Risk.
Name(s): Zhou, Chenchen, author
Kercheval, Alec N., professor directing dissertation
Wu, Wei, university representative
Ökten, Giray, committee member
Fahim, Arash, committee member
Florida State University, degree granting institution
College of Arts and Sciences, degree granting college
Department of Mathematics, degree granting department
Type of Resource: text
Genre: Text
Doctoral Thesis
Issuance: monographic
Date Issued: 2017
Publisher: Florida State University
Place of Publication: Tallahassee, Florida
Physical Form: computer
online resource
Extent: 1 online resource (128 pages)
Language(s): English
Abstract/Description: This dissertation is based on the structural model framework for default risk that was first introduced by garreau2016structural (henceforth: the "G-K model"). In this approach, the time of default is defined as the first time the log-return of the firm's stock price jumps below a (possibly stochastic) "default threshold'' level. The stock price is assumed to follow an exponential L\'evy process and, in the multidimensional case, a multidimensional L\'evy process. This new structural model is mathematically equivalent to an intensity-based model where the intensity is parameterized by a L\'evy measure. The dependence between the default times of firms within a basket is the result of the jump dependence of their respective stock prices and described by a L\'evy copula. To extend the previous work, we focus on generalizing the joint survival probability and related results to the d-dimensional case. Using the link between L\'evy processes and multivariate exponential distributions, we derive the joint survival probability and characterize correlated default risk using L\'evy copulas. In addition, we extend our results to include stochastic interest rates. Moreover, we describe how to use the default threshold as the interface for incorporating additional exogenous economic factors, and still derive basket credit default swap (CDS) prices in terms of expectations. If we make some additional modeling assumptions such that the default intensities become affine processes, we obtain explicit formulas for the single name and first-to-default (FtD) basket CDS prices, up to quadrature.
Identifier: FSU_SUMMER2017_Zhou_fsu_0071E_14012 (IID)
Submitted Note: A Dissertation submitted to the Department of Mathematics in partial fulfillment of the requirements for the degree of Doctor of Philosophy.
Degree Awarded: Summer Semester 2017.
Date of Defense: June 15, 2017.
Keywords: credit default swap, credit risk, L\'evy processes
Bibliography Note: Includes bibliographical references.
Advisory Committee: Alec N. Kercheval, Professor Directing Dissertation; Wei Wu, University Representative; Giray Okten, Committee Member; Arash Fahim, Committee Member.
Subject(s): Mathematics
Persistent Link to This Record:
Owner Institution: FSU

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Zhou, C. (2017). On the Multidimensional Default Threshold Model for Credit Risk. Retrieved from