BFS 2002

Contributed Talk

Weighted local time for fractional Brownian motion and applications to finance

Bernt Øksendal, Yaozhong Hu, Donna Mary Salopek

A Meyer-Tanaka formula involving weighted local time is derived for fractional Brownian motion and geometric fractional Brownian motion. The formula is applied to the study of the stop-loss-start-gain (SLSG) portfolio in a fractional Black-Scholes market. As a consequence, we abotain a fractional version of the Carr-Jarrow decomposition of the European call and put option prices into their intrinsic and time values.