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Consols In the Cir Model


  • Freddy Delsaen


A consol is a default-free financial instrument paying a constant stream of one unit of money. A synonym is a perpetuity. the valuation of a consol presents a particular difficulty: the time horizon of this instrument is infinity, and hence the usual technique of replacing the physical probability measure by a new probability measure represents serious problems with regard to absolute continuity of the two measures. We will work out explicit formulas when the instantaneous riskless interest rate follows a square-root process under the risk-free measure. Several mathematical properties will be investigated. Yor and Geman and Yor have considered the problem of pricing consols and carry out a more fundamental analysis (see References). This paper is self-contained and emphasizes properties or techniques not covered by those authors. Copyright 1993 Blackwell Publishers.

Suggested Citation

  • Freddy Delsaen, 1993. "Consols In the Cir Model," Mathematical Finance, Wiley Blackwell, vol. 3(2), pages 125-134.
  • Handle: RePEc:bla:mathfi:v:3:y:1993:i:2:p:125-134

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