Financial Models with Defaultable Numéraires

Travis Fisher (1) , Sergio Pulido (2, 3) , Johannes Ruf (4)

1 Aucune
2 ENSIIE - Ecole Nationale Supérieure d'Informatique pour l'Industrie et l'Entreprise
3 LaMME - Laboratoire de Mathématiques et Modélisation d'Evry
4 UCL - University College of London [London]

Financial models are studied where each asset may potentially lose value relative to any other. To this end, the paradigm of a predetermined numéraire is abandoned in favour of a symmetrical point of view where all assets have equal priority. This approach yields novel versions of the Fundamental Theorems of Asset Pricing, which clarify and extend non-classical pricing formulas used in the financial community. Furthermore, conditioning on non-devaluation, each asset can serve as proper numéraire and a classical no-arbitrage condition can be formulated. It is shown when and how these local conditions can be aggregated to a global no-arbitrage condition.

Mots clés: Defaultable numéraire; Devaluation; Fundamental Theorem of Asset Pricing; Non-classical pricing formulas

Domaines: Pricing [q-fin.PR]; Finance quantitative [q-fin.CP]; Probabilités [math.PR]

Travis Fisher, Sergio Pulido, Johannes Ruf. Financial Models with Defaultable Numéraires. 2015. ⟨hal-01240736v1⟩