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Pricing commodity-linked bonds with stochastic convenience yield, interest rate and counterparty credit risk: application of Mellin transform methods

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Listed:
  • Zonggang Ma

    (Guangdong University of Finance and Economics)

  • Chaoqun Ma

    (Hunan University)

  • Zhijian Wu

    (University of Nevada Las Vegas)

Abstract

This paper investigates the effects of the spot underlying commodity price, stochastic convenience yield, interest rate and counterparty credit risk on the pricing of the commodity-linked bonds. The stochastic factors or state variables in the model are the spot price of the underlying commodity follows geometrical Brownian motion process with a stochastic drift, the net convenience yield and the short-term interest rate are formulated as a mean-reverting Ornstein–Uhlenbeck stochastic process and the value of the firm issuing the bonds follows a geometrical Brownian motion process. Furthermore, we develop the two- and three-factor(I, II) pricing models for valuing the commodity-linked bonds. Closed-form pricing formulas of the commodity-linked bonds are derived based on the Mellin transform techniques, which are simply provided with standard (bivariate) normal cumulative distribution function so that the pricing and hedging of the commodity-linked bonds can be computed very accurately and rapidly. At last, numerical analysis compares the results of this four pricing models with realistic parameter values and demonstrates how the spot underlying commodity price, convenience yield, interest rate and counterparty credit risk affect the values of the commodity-linked bonds.

Suggested Citation

  • Zonggang Ma & Chaoqun Ma & Zhijian Wu, 2022. "Pricing commodity-linked bonds with stochastic convenience yield, interest rate and counterparty credit risk: application of Mellin transform methods," Review of Derivatives Research, Springer, vol. 25(1), pages 47-91, April.
    • Handle: RePEc:kap:revdev:v:25:y:2022:i:1:d:10.1007_s11147-021-09181-9
    DOI: 10.1007/s11147-021-09181-9
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    More about this item

    Keywords

    Commodity-linked bonds; Convenience yield; Credit risk; Pricing; Mellin transform;
    All these keywords.

    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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