Fractional Brownian motion and applications

This seminar was given 25 May 2009 as part of the PhD seminar series organised by the School of Economics & Finance of the University of St Andrews.

The fractional Brownian motion (fBm) is an extension of the classical Brownian motion that allows its disjoint increments to be correlated. In the last decade, and motivated by empirical results, several authors have studied models driven by the fBm. This seminar introduces the basic concepts and techniques regarding fBm, and discusses some of its applications in finance (how it can be used to describe the long and the short-time behaviour of the implied volatility) and physics (its connection with fractal analysis in surface growth modeling).

Videos are in MP4 format. Handouts are PDF.

Morning video 1 (50 minutes) Part I - Dr Alos introduces the concept of Fractional Brownian motions (fBm). Download MP4 | (slides 1 - 21)

Morning video 2 (42 minutes) - End of Part I and Part 2. Dr Alos develops the application of these motions in finance. Download MP4 | (slides 22 - 47)

About the Speaker

Dr Elisa Alos is Associate Professor in the Faculty of Economics at the University Pompeu Fabra (Spain). Her research interests lie in stochastic calculus, stochastic partial differential equations and mathematical finance.