A fully non-linear PDE problem  from pricing CDS withcounterparty risk

Bei Hu; Lishang Jiang; Jin Liang; Wei Wei

doi:10.3934/dcdsb.2012.17.2001

Article Contents

2012, Volume 17, Issue 6: 2001-2016. Doi: 10.3934/dcdsb.2012.17.2001

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A fully non-linear PDE problem from pricing CDS with counterparty risk

1.
Department of Applied and Computational Mathematics and Statistics, University of Notre Dame, Notre Dame, IN 46556
2.
Department of Mathematics, Tongji University, Shanghai 200092

Received: June 30, 2011

Revised: August 31, 2011

Published: August 2012

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Abstract

In this study, we establish a financial credit derivative pricing model for a contract which is subject to counterparty risks. The model leads to a fully nonlinear partial differential equation problem. We study this PDE problem and obtained a solution as the limit of a sequence of semi-linear PDE problems which also arise from financial models. Moreover, the problems and methods build a bridge between two main risk frameworks: structure and intensity models. We obtain the uniqueness, regularities and some properties of the solution of this problem.

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Mathematics Subject Classification: 35M99, 91G80.

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