On Approximation of Average Expectation Prices for Path Dependent Options in Fractional Models

Using integral representation of a fractional Brownian motion (fBm) we propose a new method of approximation of its trajectories as well as trajectories of a geometric fBm. We give the rate of convergence in \(\mathbb{L}^\textit{p}\)-norm of the approximation. Applications to pricing of path dependent options in a fractional model are considered. Lookback and Asian options are examined in detail.