He, Peng
(2016)
Mathematical Analysis of Credit Default Swaps.
Doctoral Dissertation, University of Pittsburgh.
(Unpublished)
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Unpublished |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: |
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ETD Committee: |
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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 |
Last Modified: |
15 Nov 2016 14:32 |
URI: |
http://d-scholarship.pitt.edu/id/eprint/27289 |
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