Stochastic processes are widely used for model building in the social, physical, engineering
and life sciences as well as in financial economics. In model building, statistical inference for …

Long-memory, or more generally fractal, processes are known to play an important role in
many scientific disciplines and applied fields such as physics, geophysics, hydrology …

During the seven years that elapsed between the first and second editions of the present
book, considerable progress was achieved in the area of financial modelling and pricing of …

For every value of the Hurst index H∈(0, 1) we define a stochastic integral with respect to
fractional Brownian motion of index H. We do so by approximating fractional Brownian …

In the second part of the past decade, the usage of fractional Brownian motion for financial
models was stuck. The favorable time-series properties of fractional Brownian motion …

The aim of this work is to advocate the use of multifractional Brownian motion (mBm) as a
relevant model in financial mathematics. mBm is an extension of fractional Brownian motion …

A new framework for pricing the European currency option is developed in the case where
the spot exchange rate fellows a fractional Brownian motion with jumps. An analytic formula …

Mandelbrot and van Ness (1968) suggested fractional Brownian motion as a parsimonious
model for the dynamics of? nancial price data, which allows for dependence between …

The fractional Brownian motion (fBm) extends the standard Brownian motion by introducing
some dependence between non-overlapping increments. Consequently, if one considers for …

Pricing derivatives goes back to the acclaimed Black and Scholes model. However, such a
modelling approach is known not to be able to reproduce some of the financial stylised facts …