Super-replication of European options with a derivative asset under constrained finite variation strategies

Benjamin Bruder (1)

1 LPMA - Laboratoire de Probabilités et Modèles Aléatoires

We consider a financial market, in which a first asset will be referred as the underlying and the second one as a derivative. In this market, the volatility on the underlying depends of the price of the derivative. Furthermore, the derivative is constrained to be traded with finite variation strategies. We study the super-replication problem of an European option on the underlying, and characterize its price as the unique viscosity solution of a partial differential equation with appropriate boundary conditions. We also give a dual representation of the price, as the supremum of the risk neutral expectation over a range of dynamics of the price of the derivative.

Keywords: double stochastic integrals; Gamma constraints; super-replication; viscosity solutions

Domains: Probability [math.PR]

Benjamin Bruder. Super-replication of European options with a derivative asset under constrained finite variation strategies. 2005. ⟨hal-00012183⟩