Valuation of Commodity-Linked Bond with Stochastic Convenience Yield, Stochastic Volatility, and Credit Risk in an Intensity-Based Model

Abstract

In this study, we consider an intensity-based model for pricing a commodity-linked bond with credit risk. Recently, the pricing of a commodity-linked bond with credit risk under the structural model has been studied. We extend the result using an intensity-based model, stochastic volatility model, and stochastic convenience yield model. In the intensity-based model, the credit event by the counterparty occurs at the time of first jump in a stochastic Poisson process, in which intensity is modeled as the sum of two CIR prosesses. We assume that the underlying asset follows the stochastic volatility and convenience yield models. Using the measure change technique, we explicitly derive the commodity-linked bond pricing formula in the proposed model. As a result, we provide the explicit solution for the price of the commodity-linked bond with stochastic convenience yield, stochastic volatility, and credit risk as single integrations. In addition, we present several examples to demonstrate the effects of significant parameters on the value of commodity-linked bond using numerical integration. In particular, examples are provided, focusing on the behavior of prices based on effects of recovery rate.