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Pricing Credit Default Swaps with Counterparty Risks

Zhao, Shuai (2018) Pricing Credit Default Swaps with Counterparty Risks. Doctoral Dissertation, University of Pittsburgh. (Unpublished)

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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Status: Unpublished
CreatorsEmailPitt UsernameORCID
Zhao, Shuaishz40@pitt.edushz40
ETD Committee:
TitleMemberEmail AddressPitt UsernameORCID
Committee ChairChen, Xinfuxinfu@pitt.eduxinfu
Committee MemberChen, Mingmingchen@pitt.edumingchen
Committee MemberJiang, Huiqianghqjiang@pitt.eduhqjiang
Committee MemberBeresteanu, Ariearie@pitt.eduarie
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


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