Pricing and Hedging Basis Risk under No Good Deal Assumption

Laurence Carassus (1) , Emmanuel Temam (1)

1 LPMA - Laboratoire de Probabilités et Modèles Aléatoires

We consider the problem of pricing and hedging an option written on a non-exchangeable asset when trading in a correlated asset is possible. This is a typical case of incomplete market where it is well known that the super-replication concept provides generally too high prices. Here, following J.H. Cochrane and J. Saá-Requejo, we study valuation under No Good Deal (NGD) Assumption. First, we clarify the notion of NGD for dynamic strategies, compute a lower and an upper bound and prove that in fact NGD price can be strictly higher that the one previously compute in the literature. We also propose a hedging strategy by imposing criterium on the variance of the replication's error. Finally, we provide various numerical illustrations showing the efficiency of NGD pricing and hedging.

Domaines: Gestion des risques [q-fin.RM]; Finance [q-fin.GN]

Laurence Carassus, Emmanuel Temam. Pricing and Hedging Basis Risk under No Good Deal Assumption. 2010. ⟨hal-00498479v1⟩