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. / A Dissertation submitted to the Department of Mathematics in partial fulfillment of the requirements for the degree of Doctor of Philosophy. / Summer Semester 2017. / June 15, 2017. / credit default swap, credit risk, L\'evy processes / Includes bibliographical references. / Alec N. Kercheval, Professor Directing Dissertation; Wei Wu, University Representative; Giray Okten, Committee Member; Arash Fahim, Committee Member.
| Identifer | oai:union.ndltd.org:fsu.edu/oai:fsu.digital.flvc.org:fsu_552158 |
| Contributors | Zhou, Chenchen (authoraut), 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 departmentdgg) |
| Publisher | Florida State University |
| Source Sets | Florida State University |
| Language | English, English |
| Detected Language | English |
| Type | Text, text, doctoral thesis |
| Format | 1 online resource (128 pages), computer, application/pdf |
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