Evaluation of Geometric Asian Power Options under Fractional Brownian Motion

The valuation of currency options by fractional Brownian motion

This research aims to investigate a model for pricing of currency options in which value governed by the fractional Brownian motion model (FBM). The fractional partial differential equation and some Greeks are also obtained. In addition, some properties of our pricing formula and simulation studies are presented, which demonstrate that the FBM model is easy to use.

Convergence of weighted power variations of fractional Brownian motion

The first part of the paper contains the study of the convergence for some weighted power variations of a fractional Brownian motion B with Hurst index H ∈ (0, 1). The behaviour is different when H < 1/2 and powers are odd, compared with the case when H = 1/2 or when H > 1/2 and powers are even. In the second part, one applies the results of the first part to compute the exact rate of convergen...

Fluctuations of the power variation of iterated fractional Brownian motion

We study the fluctuations of the power variation of the iterated fractional Brownian motion.

Lacunary Fractional Brownian Motion

In this paper, a new class of Gaussian field is introduced called Lacunary Fractional Brownian Motion. Surprisingly we show that usually their tangent fields are not unique at every point. We also investigate the smoothness of the sample paths of Lacunary Fractional Brownian Motion using wavelet analysis.

Tempered fractional Brownian motion