Haar Wavelets Systems for Hedging Financial Derivatives

We present a new discretization of financial instruments in terms of martingale expansions constructed using Haar wavelets systems. Examples of these systems are constructed which illustrate the discrete, spacewise, nature of the approximations. We emphasize the issue of efficient approximations and remark that expansions on these bases give the pointwise convergence needed in several applications. In particular, we work out the details of an application to hedging an European portfolio of options. We describe natural conditions under which our Haar hedging strategy can be realized by means of a self financing portfolio consisting of binary options.