# Transferable credit default swaps with counterparty risks

Liu, Jing (2019) Transferable credit default swaps with counterparty risks. Doctoral Dissertation, University of Pittsburgh. (Unpublished)

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## 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Status: Unpublished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:
Liu, Jingjil156@pitt.eduJIL156
ETD Committee:
Committee ChairChen, Xinfuxinfu@pitt.eduXINFU
Committee CoChairYao, Songsongyao@pitt.eduSONGYAO
Committee MemberRichard, Jean-Francoisfantin@pitt.eduFANTIN
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
URI: http://d-scholarship.pitt.edu/id/eprint/35826