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Author | Li, Wang |

Title | Default contagion modelling and counterparty credit risk |

URL | https://www.research.manchester.ac.uk/portal/en/theses/default-contagion-modelling-and-counterparty-credit-risk(76eee42a-d83d-4af9-956e-050615298b65).html https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.727974 |

Publication Date | 2017 |

Degree | PhD |

Degree Level | doctoral |

University/Publisher | University of Manchester |

Abstract | This thesis introduces models for pricing credit default swaps (CDS) and evaluating the counterparty risk when buying a CDS in the over-the-counter (OTC) market from a counterpart subjected to default risk. Rather than assuming that the default of the referencing firm of the CDS is independent of the trading parties in the CDS, this thesis proposes models that capture the default correlation amongst the three parties involved in the trade, namely the referencing firm, the buyer and the seller. We investigate how the counterparty risk that CDS buyers face can be affected by default correlation and how their balance sheet could be influenced by the changes in counterparty risk. The correlation of corporate default events has been frequently observed in credit markets due to the close business relationships of certain firms in the economy. One of the many mathematical approaches to model that correlation is default contagion. We propose an innovative model of default contagion which provides more flexibility by allowing the affected firm to recover from a default contagion event. We give a detailed derivation of the partial differential equations (PDE) for valuing both the CDS and the credit value adjustment (CVA). Numerical techniques are exploited to solve these PDEs. We compare our model against other models from the literature when measuring the CVA of an OTC CDS when the default risk of the referencing firm and the CDS seller is correlated. Further, the model is extended to incorporate economy-wide events that will damage all firms' credit at the same time-this is another kind of default correlation. Advanced numerical techniques are proposed to solve the resulting partial-integro differential equations (PIDE). We focus on investigating the different role of default contagion and economy-wide events have in terms of shaping the default correlation and counterparty risk. We complete the study by extending the model to include bilateral counterparty risk, which considers the default of the buyer and the correlation among the three parties. Again, our extension leads to a higher-dimensional problem that we must tackle with hybrid numerical schemes. The CVA and debit value adjustment (DVA) are analysed in detail and we are able to value the profit and loss to the investor's balance sheet due to CVA and DVA profit and loss under different market circumstances including default contagion. |

Subjects/Keywords | 332.7; PDE and PIDE ; Hybrid Numerical Schemes ; Finite-difference Numerical Schemes ; Counterparty Credit Risk ; Default Contagion Modelling ; CVA and DVA |

Rights | Full text available |

Country of Publication | uk |

Record ID | oai:ethos.bl.uk:727974 |

Repository | ethos |

Date Indexed | 2020-06-17 |

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…considers the default of the buyer and the correlation among the three
parties. Again, our extension leads to a higher-dimensional problem that we must
tackle with *hybrid* numerical *schemes*. The CVA and debit value adjustment (DVA) are
analysed in…

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- Zhou, C. “The Term Structure of Credit Spreads with Jump Risk.” Journal of Banking and Finance, (2001). Appendix A ADI scheme Parameters for CVA n − αi,j Yi−1,j +( n n − βi,j )Yi,j − γi,j Yi+1,j = Zi,j 0.5∆t (A.1) where + j Ui,j + εj Ui,j+1 + ηi,j + fi,j . 0.5∆t Zi,j = δj Ui,j−1 + Solutions Yi,j are the intermediate solutions. At the second half step, we estimate J-direction at the unknown time step and I-direction at the known time step, which leads to n − δi,j Ui,j−1 +( n n − i,j )Ui,j − εi,j Ui,j+1 = Z̃i,j , 0.5∆t (A.2) where Z̃i,j = αi Ui−1,j + ( + βj )Ui,j + γj Ui+1,j + ηi,j + fi,j . 0.5∆t The coefficients given by γi=0 = κ1 (θ1 − i∆λ1 ) 0.5σ12 i∆λ1 κ1 (θ1 − i∆λ1 ) + , αi=I = − 2∆λ1 ∆λ1 2∆λ1 κ1 (θ1 − i∆λ1 ) 0.5σ1 i∆λ1 γi = − + , γi=I = 0 2∆λ1 ∆λ21 αi = − αi=0 = 0 , κ1 θ1 , 2∆λ1 κ1 θ1 (r + j∆λ2 ) κ2 θ2 (r + i∆λ1 ) − , j=0 = − − ∆λ1 ∆λ2 0.5σ1 i∆λ1 (r + i∆λ1 + j∆λ2 ) 0.5σ2 j∆λ2 (r + i∆λ1 + j∆λ2 ) βi = −2 − , j = −2 − ∆λ1 ∆λ22 κ1 (θ1 − i∆λ1 ) (r + i∆λ1 + j∆λ2 ) κ2 (θ2 − j∆λ2 ) (r + i∆λ1 + j∆λ2 ) βI = − , j=J = − ∆λ1 ∆λ2 βi=0 = −