Stochastic integration w.r.t. fractional Brownian motion (fBm) has raised strong interest in recent years, motivated in particular by applications in finance and Internet traffic modelling. Since fBm is not a semi-martingale, stochastic integration requires specific developments. Multifractional...

The generalized multifractional Brownian motion (GMBM) is a continuous Gaussian process that extends the classical fractional Brownian motion (FBM) and multifractional Brownian motion (MBM) (SIAM Rev. 10 (1968) 422; INRIA Res. Rept. 2645 (1995); Rev. Mat. Iberoamericana 13 (1997) 19; Fractals: Theory...

This paper is devoted to the application of B-splines to volatility modeling, specifically the calibration of the leverage function in stochastic local volatility models and the parameterization of an arbitrage-free implied volatility surface calibrated to sparse option data. We use an extension...

A lot is known about the Hölder regularity of stochastic processes, in particular in the case of Gaussian processes. Recently, a finer analysis of the local regularity of functions, termed 2-microlocal analysis, has been introduced in a deterministic frame: through the computation of the...