Some of the material in is restricted to members of the community. By logging in, you may be able to gain additional access to certain collections or items. If you have questions about access or logging in, please use the form on the Contact Page.
The default threshold framework for credit risk modeling developed by Garreau and Kercheval [SIAM Journal on Financial Mathematics, 7:642-673, 2016] enjoys the advantages of both the structural form models and the reduced form models, including excellent analytical tractability. In their paper, the closed form default time distribution of a company is derived when the default threshold is a constant or a deterministic function. As for stochastic default threshold, it is shown that the survival probability can be derived as an expectation. How to specify the stochastic default threshold so that this expectation can be obtained in closed form is however left unanswered. The purpose of this thesis is to fulfill this gap. In this thesis, three credit risk models with stochastic default thresholds are proposed, under each of which the closed form default time distribution is derived. Unlike Garreau and Kercheval's work where the log-return of a company's stock price is assumed to be independent and identically distributed and the interest rate is assumed constant, in our new proposed models the random interest rate and the stochastic volatility of a company's stock price are taken into consideration. While in some cases the defaultable bond price, the credit spread and the CDS premium are derived in closed form under the new proposed models, in others it seems not so easy. The difficulty that stops us from getting closed form formulas is also discussed in this thesis. Our new models involve the Heston model, which has a closed form characteristic function. We found the common characteristic function formula used in the literature not always applicable for all input variables. In this thesis the safe region of the formula is analyzed completely. A new formula is also derived that can be used to find the characteristic function value in some cases when the common formula is not applicable. An example is given where the common formula fails and one should use the new formula.
Credit risk, Default level, Default threshold, Levy process
Date of Defense
November 15, 2016.
A Dissertation submitted to the Department of Mathematics in partial fulfillment of the requirements for the degree of Doctor of Philosophy.
Includes bibliographical references.
Alec Kercheval, Professor Directing Dissertation; Eric Chicken, University Representative; Giray Okten, Committee Member; Arash Fahim, Committee Member.
Florida State University
Use and Reproduction
This Item is protected by copyright and/or related rights. You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s). The copyright in theses and dissertations completed at Florida State University is held by the students who author them.