English

Black to Negative: Embedded optionalities in commodities markets

Pricing of Securities 2020-10-30 v2 Risk Management

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.

Keywords

Cite

@article{arxiv.2006.06076,
  title  = {Black to Negative: Embedded optionalities in commodities markets},
  author = {Richard J. Martin and Aldous Birchall},
  journal= {arXiv preprint arXiv:2006.06076},
  year   = {2020}
}

Comments

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

R2 v1 2026-06-23T16:13:12.490Z