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Explicit solution of an inverse first-passage time problem for L\'{e}vy processes and counterparty credit risk

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  • M. H. A. Davis
  • M. R. Pistorius

Abstract

For a given Markov process $X$ and survival function $\overline{H}$ on $\mathbb{R}^+$, the inverse first-passage time problem (IFPT) is to find a barrier function $b:\mathbb{R}^+\to[-\infty,+\infty]$ such that the survival function of the first-passage time $\tau_b=\inf \{t\ge0:X(t)

Suggested Citation

  • M. H. A. Davis & M. R. Pistorius, 2013. "Explicit solution of an inverse first-passage time problem for L\'{e}vy processes and counterparty credit risk," Papers 1306.2719, arXiv.org, revised Sep 2015.
    • Handle: RePEc:arx:papers:1306.2719
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    File URL: http://arxiv.org/pdf/1306.2719
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    References listed on IDEAS

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    1. Merton, Robert C, 1974. "On the Pricing of Corporate Debt: The Risk Structure of Interest Rates," Journal of Finance, American Finance Association, vol. 29(2), pages 449-470, May.
    2. Black, Fischer & Cox, John C, 1976. "Valuing Corporate Securities: Some Effects of Bond Indenture Provisions," Journal of Finance, American Finance Association, vol. 31(2), pages 351-367, May.
    3. Christophette Blanchet-Scalliet & Fr'ed'eric Patras, 2008. "Counterparty risk valuation for CDS," Papers 0807.0309, arXiv.org.
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    Cited by:

    1. Jan Obłój & Thaleia Zariphopoulou, 2021. "In memoriam: Mark H. A. Davis and his contributions to mathematical finance," Mathematical Finance, Wiley Blackwell, vol. 31(4), pages 1099-1110, October.

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