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Asymptotic approximation of the hitting-time and evaluation of a risky bond

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  • Ahmed Loulit

Abstract

In this paper, we give an approximation for the density of the first–passage time through a boundary defined by smooth function S(t). The density is a solution of some Voltera integral and admits an expansion of the Neumann-type series, and the error term converges rapidly to zero. We examine the case of a non homogeneous-time Brownian diffusion which is related to the evaluation of many claims on financial asset. An application to the approximated valuation of risky bonds and options on the asset of levered firm is provided.

Suggested Citation

  • Ahmed Loulit, 2004. "Asymptotic approximation of the hitting-time and evaluation of a risky bond," Working Papers CEB 04-029.RS, ULB -- Universite Libre de Bruxelles.
    • Handle: RePEc:sol:wpaper:04-029
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    References listed on IDEAS

    as
    1. Leland, Hayne E & Toft, Klaus Bjerre, 1996. "Optimal Capital Structure, Endogenous Bankruptcy, and the Term Structure of Credit Spreads," Journal of Finance, American Finance Association, vol. 51(3), pages 987-1019, July.
    2. Longstaff, Francis A & Schwartz, Eduardo S, 1995. "A Simple Approach to Valuing Risky Fixed and Floating Rate Debt," Journal of Finance, American Finance Association, vol. 50(3), pages 789-819, July.
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    More about this item

    Keywords

    hitting-time; Brownian diffusion; levered firm.;
    All these keywords.

    JEL classification:

    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • C40 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - General

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