Consols In the Cir Model

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. Copyright 1993 Blackwell Publishers.

A general proof of the Dybvig-Ingersoll-Ross theorem: long forward rates can never fall

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“…There are several ways 8 to recover this value (see Delbaen (1993) and Geman and Yor (1993)) but a useful formulation given by Delbaen (1993, pg. 129) is…”

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