A model-free approach to delta hedging

provided by Research Papers in Economics

inria-00457222, version 1 - 16 Feb 2010

A model-free approach to delta hedging

Michel Fliess^1,2 and Cedric Join^1,3

¹ INRIA-ALIEN

² LIX (CNRS, UMR 7161), Ecole polytechnique
91128 Palaiseau, France

[email protected]

³ CRAN (CNRS, UMR 7039), Nancy-Universite
BP 239, 54506 Vandœuvre-les-Nancy, France

[email protected]

Abstract

Delta hedging, which plays a crucial role in modern financial engi-
neering, is a tracking control design for a “risk-free” management. We
utilize the existence of trends for financial time series (Fliess M., Join C.:
A mathematical proof of the existence of trends in financial time series,
Proc. Int. Conf. Systems Theory: Modelling, Analysis and Control,
Fes, 2009. Online: http://hal.inria.fr/inria-00352834/en/) in order
to propose a model-free setting for delta hedging. It avoids most of the
shortcomings encountered with the now classic Black-Scholes-Merton set-
ting. Several convincing computer simulations are presented. Some of
them are dealing with abrupt changes, i.e., jumps.

Keywords—Delta hedging, trends, quick fluctuations, abrupt changes,
jumps, tracking control, model-free control.