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Arbitrage valuation and bounds for sinking-fund bonds with multiple sinking-fund dates

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  • Anna Rita Bacinello
  • Fulvio Ortu

Abstract

The paper tackles the problem of pricing, under interest-rate risk, a default-free sinking-fund bond which allows its issuer to recurrently retire part of the issue by (a) a lottery call at par, or (b) an open market repurchase. By directly modelling zero-coupon bonds as diffusions driven by a single-dimensional Brownian motion, a pricing formula is supplied for the sinking-fund bond based on a backward induction procedure which exploits, at each step, the martingale approach to the valuation of contingent-claims. With more than one sinking-fund date, however, the pricing formula is not in closed form, not even for simple parametrizations of the process for zerocoupon bonds, so that a numerical approach is needed. Since the computational complexity increases exponentially with the number of sinking-fund dates, arbitrage-based lower and upper bounds are provided for the sinking-fund bond price. The computation of these bounds is almost effortless when zero-coupon bonds are as described by Cox, Ingersoll and Ross. Numerical comparisons between the price of the sinking-fund bond obtained via Monte Carlo simulation and these lower and upper bounds are illustrated for different choices of parameters.

Suggested Citation

  • Anna Rita Bacinello & Fulvio Ortu, 1999. "Arbitrage valuation and bounds for sinking-fund bonds with multiple sinking-fund dates," Applied Mathematical Finance, Taylor & Francis Journals, vol. 6(4), pages 293-312.
    • Handle: RePEc:taf:apmtfi:v:6:y:1999:i:4:p:293-312
    DOI: 10.1080/13504869950079301
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    References listed on IDEAS

    as
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