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A correction note on the first passage time of an Ornstein-Uhlenbeck process to a boundary


  • O. Renault

    () (Département des Sciences Economiques, Université Catholique de Louvain, 3 Place Montesquieu, B-1348 Louvain-la-Neuve, Belgique)

  • O. Scaillet

    () (Département des Sciences Economiques, Université Catholique de Louvain, 3 Place Montesquieu, B-1348 Louvain-la-Neuve, Belgique)

  • B. Leblanc

    () (Banque Nationale de Paris, BFI-MC, 13, rue Lafayette, F-75009 Paris, France)


This paper provides the derivation of the hitting time density of an Ornstein-Uhlenbeck process to a flat boundary. The derivation relies on a change of measure approach and delivers an explicit formula. This formula is an amended expression of the result given in Leblanc and Scaillet (1998). It corresponds to the formula given by a time substitution approach when the boundary level coincides with the mean of the invariant measure. It can for example be used to price digital up-and-in credit spread options when the logarithm of the credit spread is assumed to follow an Ornstein-Uhlenbeck process.

Suggested Citation

  • O. Renault & O. Scaillet & B. Leblanc, 2000. "A correction note on the first passage time of an Ornstein-Uhlenbeck process to a boundary," Finance and Stochastics, Springer, vol. 4(1), pages 109-111.
  • Handle: RePEc:spr:finsto:v:4:y:2000:i:1:p:109-111 Note: received: February 1999; final version received: April 1999

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    References listed on IDEAS

    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.
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    Cited by:

    1. Hidetoshi Nakagawa & Tomoaki Shouda, 2004. "Analyses of Mortgage-Backed Securities Based on Unobservable Prepayment Cost Processes," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 11(3), pages 233-266, September.

    More about this item


    Hitting time; Ornstein-Uhlenbeck process; path dependent option;

    JEL classification:

    • E43 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Interest Rates: Determination, Term Structure, and Effects
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing


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