Mathematical Analysis of Credit Default Swaps

He, Peng (2016) Mathematical Analysis of Credit Default Swaps. Doctoral Dissertation, University of Pittsburgh. (Unpublished)

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Abstract

In this thesis, we establish a financial credit derivative pricing model for a credit default swap (CDS) contract which is subject to counterparty risks. A credit default swap is an agreement on exchange of cash flows between two parties, the buyer and the seller, about the occurrence of a credit event. The buyer makes a series of payments to the seller before the event and before the expiration date. The seller pays the buyer a fixed compensation at the moment when the event occurs, if it is before the expiry. The model arises a linear partial differential equation problem. We study this model, i.e. differential equation and show that a solution of the PDE problem from structure model can be obtained as the limit of a sequence of PDE problems which comes from intensity model. In addition, we study the infinite horizon problem of the pricing model which leads to a nonlinear ordinary differential equation problem. We obtain a implicit solution of the ODE problem and prove the solution can be converged by the solution of the PDE problem exponentially. Furthermore, the models and theoretical methods in this study get connected between two main risk frameworks: term structure model and intensity model, which greatly extend the area of applicability of structure models in financial problems. Moreover, We obtain the uniqueness, existence, and properties of the solutions of the PDE and ODE problems. Nevertheless, we implement numerical methods to calibrate the parameters of stochastic interest rate model and analyze the numerical solutions of the pricing model.

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Details

Item Type: University of Pittsburgh ETD
Status: Unpublished
Creators/Authors:
He, Pengpeh33@pitt.eduPEH33
ETD Committee:
Committee ChairChen, xinfuxinfu@pitt.eduXINFU
Committee MemberIyengar, satishssi@pitt.eduSSI
Committee MemberChen, mingmingchen@pitt.eduMINGCHEN
Date: 6 June 2016
Date Type: Publication
Defense Date: 30 March 2016
Approval Date: 6 June 2016
Submission Date: 21 March 2016
Access Restriction: No restriction; Release the ETD for access worldwide immediately.
Number of Pages: 69
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: Structure model, counterparty risk, linear PDE, infinite horizon, numerical analysis
Date Deposited: 06 Jun 2016 16:20