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Consols In the Cir Model

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  • Freddy Delsaen

Abstract

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.

Suggested Citation

  • Freddy Delsaen, 1993. "Consols In the Cir Model," Mathematical Finance, Wiley Blackwell, vol. 3(2), pages 125-134, April.
    • Handle: RePEc:bla:mathfi:v:3:y:1993:i:2:p:125-134
    DOI: 10.1111/j.1467-9965.1993.tb00082.x
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    Cited by:

    1. Angelos Dassios & Jia Wei Lim & Yan Qu, 2020. "Azéma martingales for Bessel and CIR processes and the pricing of Parisian zero‐coupon bonds," Mathematical Finance, Wiley Blackwell, vol. 30(4), pages 1497-1526, October.
    2. Dassios, Angelos & Lim, Jia Wei & Qu, Yan, 2020. "Azéma martingales for Bessel and CIR processes and the pricing of Parisian zero-coupon bonds," LSE Research Online Documents on Economics 101765, London School of Economics and Political Science, LSE Library.

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