BFS 2002

Contributed Talk

A General Fractional White Noise Theory and Applications to Finance

John van der Hoek, Robert J. Elliott

We present a new framework for fractional Brownian motion in which processes with all indices can be considered under the same probability measure. Our results extend recent contributions by Hu, Øksendal, Duncan, Pasik-Duncan and others. As an application we develop option pricing in a fractional Black-Scholes market with a noise process driven by a sum of fractional Brownian motions with various Hurst indices.