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.

本文研究了现货标的商品价格、随机便利收益率、利率和交易对手信用风险对商品挂钩债券定价的影响。模型中的随机因素或状态变量是标的商品的现货价格遵循具有随机漂移的几何布朗运动过程，净便利收益率和短期利率被公式化为均值回归的 Ornstein-Uhlenbeck 随机过程发行债券的公司的价值遵循几何布朗运动过程。此外，我们开发了两因素和三因素（I，II）定价模型来对商品挂钩债券进行估值。商品挂钩债券的封闭式定价公式是基于梅林变换技术推导出来的，简单地提供标准（双变量）正态累积分布函数，以便可以非常准确和快速地计算商品挂钩债券的定价和对冲。最后，数值分析将这四种定价模型的结果与实际参数值进行了比较，并论证了现货标的商品价格、便利收益率、利率和交易对手信用风险如何影响商品挂钩债券的价值。