|Date: Wednesday, April 11, 2018
Location: 1360 East Hall (4:00 PM to 5:00 PM)
Title: A Martingale Approach for Fractional Brownian Motions and Related Path Dependent PDEs
Abstract: Recent empirical studies show that volatility could be rough, and thus it is natural to use Fractional Brownian Motion (fBM) to model the volatility. We are interested in the derivative pricing and hedging theory in such a model. However, fBM is neither a Markov process nor a semimartingale, then many standard methods relying on PDEs and/or martingales fail in this setting. By introducing the so called forward volatility as extra state variables, we "recover" the standard theory in this setting by using path dependent PDEs. Our main tool is a new functional Ito formula, in the spirit of Dupire.
This is a joint work with Frederi Viens.
Speaker: Jianfeng Zhang