Modeling breach of contract risk through bundled options

In this paper, in order to model breach of contract risk, we design and value a bundled option that is composed of contract abandonment and price renegotiation. We show numerically that the bundled option is more valuable for the contract than either of the options, ie, contract abandonment and price renegotiation, in isolation. This value increases monotonically as the spot price becomes more volatile. The value of the bundled option is less than the sum of the individual option values, hence showing the subadditive property. We demonstrate that in the presence of high spotprice volatility, the bundled option is more valuable when the renegotiation date is selected to be closer to the half-life of the contract. We also show that early contract abandonment probability goes down in the presence of a renegotiation option. We conclude that the commodity supplier should negotiate with the buyer a supply chain contract with flexible options at the design stage, obtaining contract abandonment and price renegotiation options – as a bundled option – in order to enhance the supply contract value and reduce the breach of contract risk.