Consols In the Cir Model

Freddy Delsaen

Mathematical Finance, 1993, vol. 3, issue 2, 125-134

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.

Date: 1993
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