\`x^2+y_1+z_12^34\`
Advanced Search
Article Contents
Article Contents

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

Abstract Related Papers Cited by
  • 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.
    Mathematics Subject Classification: 35M99, 91G80.

    Citation:

    \begin{equation} \\ \end{equation}
  • [1]

    F. Black and J. Cox, Valuing corporate securities: Some effects of bond indenture provisions, Journal of Finance, 31 (1976), 351-367.doi: 10.1111/j.1540-6261.1976.tb01891.x.

    [2]

    T. Bielecki and M. Rutkowski, "Credit Risk: Modeling, Valuation and Hedging," Springer Finance, Springer-Verlag, Berlin, 2002.

    [3]

    S. Crepey, M. Jeanblanc and B. Zargari, Counterparty risk on a CDS in a Markov Chain Copula model with joint defaults, working paper, 2009.

    [4]

    J. Cox, J. Ingersoll and S. Ross, A Theory of the term structure of interest rates, Econometrica, 53 (1985), 385-407.doi: 10.2307/1911242.

    [5]

    D. Duffie and K. J. Singleton, Modeling term structures of defaultable bonds, Review of Financial Studies, 12 (1999), 687-720.doi: 10.1093/rfs/12.4.687.

    [6]

    B. Øksendal, "Stochastic Differential Equations. An Introduction with Applications," fifth edition, Universitext, Springer-Verlag, Berlin, 1998.

    [7]

    A. Friedman, "Variational Principles and Free Boundary Problems," Second edition, Robert E. Krieger Publishing Co., Inc., Malabar, FL, 1988.

    [8]

    D. Lando, On Cox processes and credit risky securities, Review of Derivatives Research, 2 (1998), 99-120.

    [9]

    F. Longstaff and E. Schwartz, A simple approach to valuing risky fixed and floating rate debt, Journal of Finance, 50 (1995), 789-819.doi: 10.2307/2329288.

    [10]

    R. Merton, On the valuing of corporate debt: The risk structure of interest rates, Journal of Finance, 29 (1974), 449-470.doi: 10.1111/j.1540-6261.1974.tb03058.x.

  • 加载中
SHARE

Article Metrics

HTML views() PDF downloads(62) Cited by(0)

Access History

Other Articles By Authors

Catalog

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return