Valuation of sinking-fund bonds in the Vasicek and CIR frameworks*Financial support from Murst Fondo 40% on 'Modelli di struttura a termine dei tassi d'interesse' is gratefully acknowledged.

In a sinking-fund bond, the issuer is required to retire portions of the bond prior to maturity, with the option of doing so either by calling the bonds by lottery, or by buying them back at their market value. This paper discusses the valuation of a default-free sinking-fund bond issue in the Vasicek (1977) and, alternatively, the Cox, Ingersoll and Ross (CIR) (1985) frameworks. We show in particular that, calling the bond issue without the delivery option 'corresponding serial', and the one without the prepayment feature 'corresponding coupon', under no-arbitrage a sinking-fund bond can be priced either in terms of the corresponding coupon bond and a bond call option, or in terms of the corresponding serial and a bond put option. We also present a detailed comparative-statics analysis of our valuation model, where we show that a sinking-fund bond has a stochastic duration intermediate between the ones of the corresponding serial and coupon bonds. We argue that such a feature gives a further rational for the presence of the delivery option. Moreover, we compare our results with the ones of Ho (1985), who has previously discussed the valuation problem under scrutiny.