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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

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  • Anna Rita Bacinello
  • Fulvio Ortu
  • Patrizia Stucchi

Abstract

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.

Suggested Citation

  • Anna Rita Bacinello & Fulvio Ortu & Patrizia Stucchi, 1996. "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," Applied Mathematical Finance, Taylor & Francis Journals, vol. 3(4), pages 269-394.
    • Handle: RePEc:taf:apmtfi:v:3:y:1996:i:4:p:269-394
    DOI: 10.1080/13504869600000013
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    References listed on IDEAS

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    1. Dunn, Kenneth B. & Spatt, Chester S., 1984. "A strategic analysis of sinking fund bonds," Journal of Financial Economics, Elsevier, vol. 13(3), pages 399-423, September.
    2. Jamshidian, Farshid, 1989. " An Exact Bond Option Formula," Journal of Finance, American Finance Association, vol. 44(1), pages 205-209, March.
    3. David Heath & Robert Jarrow & Andrew Morton, 2008. "Bond Pricing And The Term Structure Of Interest Rates: A New Methodology For Contingent Claims Valuation," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 13, pages 277-305, World Scientific Publishing Co. Pte. Ltd..
    4. Ho, Thomas & Singer, Ronald F, 1984. "The Value of Corporate Debt with a Sinking-Fund Provision," The Journal of Business, University of Chicago Press, vol. 57(3), pages 315-336, July.
    5. Ho, Thomas S Y & Lee, Sang-bin, 1986. "Term Structure Movements and Pricing Interest Rate Contingent Claims," Journal of Finance, American Finance Association, vol. 41(5), pages 1011-1029, December.
    6. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
    7. Vasicek, Oldrich Alfonso, 1977. "Abstract: An Equilibrium Characterization of the Term Structure," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 12(4), pages 627-627, November.
    8. Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1979. "Duration and the Measurement of Basis Risk," The Journal of Business, University of Chicago Press, vol. 52(1), pages 51-61, January.
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    Cited by:

    1. Marianito R. Rodrigo & Rogemar S. Mamon, 2014. "An alternative approach to the calibration of the Vasicek and CIR interest rate models via generating functions," Quantitative Finance, Taylor & Francis Journals, vol. 14(11), pages 1961-1970, November.

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