Liu, Jing
(2019)
Transferable credit default swaps with counterparty risks.
Doctoral Dissertation, University of Pittsburgh.
(Unpublished)
Abstract
A credit default swap (CDS) is a financial contract between two parties who exchange cash flows based on an occurrence of an underlying credit default (or more general, event). Under a CDS, the seller will pay a compensation to the buyer at the time of the credit event, if it happens before the expiry; in return, the buyer agrees to pay a continuous premium to the seller until the occurrence of the credit event or the expiry, whichever is earlier. Counterparty risk refers to the risk caused by the default of one party of an active contract. By transferable, it means that one party of a CDS, at the time of his default, can sell the contract to a third party. We consider three kinds of transferability: (i) transferable only by the seller at most one time; (ii) transferable by both parties at most one time; and (iii) transferable by both parties any number of times. The problem here is to price transferable CDSs with counterparty risks. We study an intensity model where the credit event and default times are described by arrival times of Poisson processes with variable intensities depending on a state variable, for definiteness, chosen as the interest rate. We model the interest rate by a classical Cox-Ingersoll-Ross model. The pricing problem is then modeled by an initial value problem of a degenerate partial differential equation (PDE) on an unbounded domain. We prove that the PDE problem is well-poseded. We also derive certain useful estimates on the bounds of the solutions. Besides the intensity model, another primary model is the structure model. We establish the connection between these two models; in particular, we show that the solution of the structure model is the limit of a sequence of solutions of the intensity models. Certain numerical simulations are also provided.
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Details
| Item Type: |
University of Pittsburgh ETD
|
| Status: |
Unpublished |
| Creators/Authors: |
|
| ETD Committee: |
|
| Date: |
20 June 2019 |
| Date Type: |
Publication |
| Defense Date: |
7 December 2018 |
| Approval Date: |
20 June 2019 |
| Submission Date: |
21 December 2018 |
| Access Restriction: |
No restriction; Release the ETD for access worldwide immediately. |
| Number of Pages: |
100 |
| 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: |
Credit default swaps, Transferable, Counterparty risk, Intensity model, Structure model, Well-posedness, CIR model |
| Date Deposited: |
20 Jun 2019 16:19 |
| Last Modified: |
20 Jun 2019 16:19 |
| URI: |
http://d-scholarship.pitt.edu/id/eprint/35826 |
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