Zhao, Shuai
(2018)
Pricing Credit Default Swaps with Counterparty Risks.
Doctoral Dissertation, University of Pittsburgh.
(Unpublished)
Abstract
A credit default swap, or CDS, is a financial agreement between two parties about an exchange of cash flows that depend on the occurrence of a credit default or in general a credit event. A CDS may terminate earlier than the expiration or the occurrence of the credit event when one party of the contract defaults, this is called counterparty risk. This thesis studies the price of CDS with counterparty risks. The credit default and counterparty risks are modeled by the first arrival times of Poisson processes with stochastic intensities depending on interest rates. The popular CIR and Vasicek models are used for interest rates in this thesis. The prices of CDS are derived as solutions of different partial differential equations with respect to the CIR and Vasicek models, respectively. For the CIR model, the volatility for the interest rate vanishes as interest rate approaches zero. New techniques are introduced here to deal with this degeneracy and cover the full parameter range, thereby allowing the usability of any empirical calibrated CIR models. For the Vasicek model, the allowance of negative interest rate can produce an arbitrarily large discount factor, instead of typically smaller than one; this poses difficulties in mathematical analysis and financial predictions. This thesis solves the mathematical well-posedness problem and more importantly, produces accurate bounds of the CDS price. For the CDS with long time to expiry, the corresponding infinite horizon problems are studied. As time to expiry goes to infinity, the price of CDS being the asymptotic limit of the solution of the infinite horizon problem is verified.
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| Item Type: |
University of Pittsburgh ETD
|
| Status: |
Unpublished |
| Creators/Authors: |
|
| ETD Committee: |
|
| Date: |
31 January 2018 |
| Date Type: |
Publication |
| Defense Date: |
7 September 2017 |
| Approval Date: |
31 January 2018 |
| Submission Date: |
5 April 2017 |
| Access Restriction: |
No restriction; Release the ETD for access worldwide immediately. |
| Number of Pages: |
73 |
| Institution: |
University of Pittsburgh |
| Schools and Programs: |
Dietrich School of Arts and Sciences > Mathematics |
| Degree: |
PhD - Doctor of Philosophy |
| Thesis Type: |
Doctoral Dissertation |
| Refereed: |
Yes |
| Uncontrolled Keywords: |
Counterparty risk, CIR, Vasicek, negative interest rate, infinite horizon problems. |
| Date Deposited: |
31 Jan 2018 19:35 |
| Last Modified: |
31 Jan 2018 19:35 |
| URI: |
http://d-scholarship.pitt.edu/id/eprint/31295 |
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