Non Quadratic Local Risk-Minimization for Hedging Contingent Claims in the Presence of Transaction Costs

Frédéric Abergel (1, 2) , Nicolas Millot (1, 2)

1 MAS - Mathématiques Appliquées aux Systèmes - EA 4037
2 FiQuant - Chaire de finance quantitative

Following up on the new criterion introduced by Abergel and Millot for hedging contingent claims in incomplete markets, we extend the approach to the case where there are transaction costs on the stock component. The local risk is a convex function of the local costs process. We derive corresponding optimal strategies in both discrete time and continuous time settings. Finally we give an application of our hedging method in the stochastic volatility case as well as in the jump diffusion case.

Domaines: Finance quantitative [q-fin.CP]

Frédéric Abergel, Nicolas Millot. Non Quadratic Local Risk-Minimization for Hedging Contingent Claims in the Presence of Transaction Costs. 2011. ⟨hal-00621256v1⟩