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

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. This revised version was published online in August 2006 with corrections to the Cover Date.