Heyde, C C2015-12-132015-12-130021-9002http://hdl.handle.net/1885/94920The geometric Brownian motion (Black-Scholes) model for the price of a risky asset stipulates that the log returns are i.i.d. Gaussian. However, typical log returns data shows a leptokurtic distribution (much higher peak and heavier tails than the Gaussian) as well as evidence of strong dependence. In this paper a subordinator model based on fractal activity time is proposed which simply explains these observed features in the data, and whose scaling properties check out well on various data sets.Keywords: Black-Scholes model; Fractal activity time; Heavy tails; Long-range dependence; Risky asset model; Self-similarity19992015-12-12