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The Pricing Formula for Commodity-Linked Bonds with Stochastic Convenience Yields and Default Risk

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  • Ryozo Miura
  • Hiroaki Yamauchi

Abstract

At the maturity, the owner of a commodity-linked bond has the right to receive the face value of the bond and the excess amount of spot market value of the reference commodity bundle over the prespecified exercise price. This payoff structure is an important characteristic of the commodity-linked bonds. In this paper, we derive closed pricing formulae for the commodity-linked bonds. We assume that the reference commodity price and the value of the firm (bonds' issuer) follow geometric Brownian motions and that the net marginal convenience yield and interest rate follow Ornstein–Uhlenbech processes. In the appendix, we derive pricing formulae for bonds which are the same as the above commodity-linked bonds, except that the reference commodity price in the definition of the payoff at the maturity is replaced by the value of a special asset which depends on the convenience yield. Copyright Kluwer Academic Publishers 1998

Suggested Citation

  • Ryozo Miura & Hiroaki Yamauchi, 1998. "The Pricing Formula for Commodity-Linked Bonds with Stochastic Convenience Yields and Default Risk," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 5(2), pages 129-158, May.
    • Handle: RePEc:kap:apfinm:v:5:y:1998:i:2:p:129-158
    DOI: 10.1023/A:1010034115552
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    References listed on IDEAS

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    1. Schwartz, Eduardo S, 1982. "The Pricing of Commodity-Linked Bonds," Journal of Finance, American Finance Association, vol. 37(2), pages 525-539, May.
    2. Carr, Peter, 1987. "A Note on the Pricing of Commodity-Linked Bonds," Journal of Finance, American Finance Association, vol. 42(4), pages 1071-1076, September.
    3. Gibson, Rajna & Schwartz, Eduardo S, 1990. "Stochastic Convenience Yield and the Pricing of Oil Contingent Claims," Journal of Finance, American Finance Association, vol. 45(3), pages 959-976, July.
    4. Nicholas Kaldor, 1939. "Speculation and Economic Stability," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 7(1), pages 1-27.
    5. Black, Fischer, 1976. "The pricing of commodity contracts," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 167-179.
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    Cited by:

    1. Samuel Malone, 2005. "Managing Default Risk for Commodity Dependent Countries: Price Hedging in an Optimizing Model," Economics Series Working Papers 246, University of Oxford, Department of Economics.
    2. Turvey, Calum G. & Chantarat, Sommarat, 2006. "Weather-Linked Bonds," 2006 Agricultural and Rural Finance Markets in Transition, October 2-3, 2006, Washington, DC 133091, Regional Research Committee NC-1014: Agricultural and Rural Finance Markets in Transition.
    3. Joseph Atta-Mensah, 2004. "Commodity-Linked Bonds: A Potential Means for Less-Developed Countries to Raise Foreign Capital," Staff Working Papers 04-20, Bank of Canada.

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