Black to Negative: Embedded optionalities in commodities markets

Abstract

We address the modelling of commodities that are supposed to have positive price but, on account of a possible failure in the physical delivery mechanism, may turn out not to. This is done by explicitly incorporating a `delivery liability' option into the contract. As such it is a simple generalisation of the established Black model.

Extended section on Levy models and given explicit formulae and numerical example. Corrected typo in put/call formulae (eq.5,6 in this vsn)