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Mathematical analysis of credit defa...

He, Peng.

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Mathematical analysis of credit default swaps.

Record Type:	Electronic resources : Monograph/item
Title/Author:	Mathematical analysis of credit default swaps./
Author:	He, Peng.
Published:	Ann Arbor : ProQuest Dissertations & Theses, : 2016,
Description:	70 p.
Notes:	Source: Dissertation Abstracts International, Volume: 78-04(E), Section: B.
Contained By:	Dissertation Abstracts International78-04B(E).
Subject:	Mathematics. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=10183715
ISBN:	9781369318395

Mathematical analysis of credit default swaps.
He, Peng.

Mathematical analysis of credit default swaps. - Ann Arbor : ProQuest Dissertations & Theses, 2016 - 70 p.

Source: Dissertation Abstracts International, Volume: 78-04(E), Section: B.

Thesis (Ph.D.)--University of Pittsburgh, 2016.

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.

ISBN: 9781369318395Subjects--Topical Terms:

515831
Mathematics.

Mathematical analysis of credit default swaps.
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020 $a 9781369318395
035 $a (MiAaPQ)AAI10183715
035 $a AAI10183715
040 $a MiAaPQ $c MiAaPQ
100 1 $a He, Peng. $3 1671791
245 1 0 $a Mathematical analysis of credit default swaps.
260 1 $a Ann Arbor : $b ProQuest Dissertations & Theses, $c 2016
300 $a 70 p.
500 $a Source: Dissertation Abstracts International, Volume: 78-04(E), Section: B.
500 $a Adviser: Xinfu Chen.
502 $a Thesis (Ph.D.)--University of Pittsburgh, 2016.
520 $a 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.
520 $a Keywords: Structure model, counterparty risk, linear PDE, infinite horizon, numerical analysis.
590 $a School code: 0178.
650 4 $a Mathematics. $3 515831
650 4 $a Applied mathematics. $3 2122814
650 4 $a Finance. $3 542899
650 4 $a Theoretical mathematics. $3 3173530
690 $a 0405
690 $a 0364
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710 2 $a University of Pittsburgh. $b Mathematics. $3 2105939
773 0 $t Dissertation Abstracts International $g 78-04B(E).
790 $a 0178
791 $a Ph.D.
792 $a 2016
793 $a English
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=10183715