Empirical realities for a minimal descriptions risky asset model

Chris Heyde, Shuangzhe Liu

Research output: Contribution to journalArticlepeer-review


The classical Geometric Brownian motion (GBM) model for the price of a risky asset, from which the huge financial derivatives industry has developed, stipulates that the log returns are iid Gaussian. however, typical log returns data show a distribution with much higher peaks and heavier tails than the Gaussian as well as evidence of strong and persistent dependence. In this paper we describe a simple replacement for GBM, a fractal activity time Geometric Brownian motion (FATGBM) model based on fractal activity time which readily explains these observed features in the data. Consequences of the model are explained, and examples are given to illustrate how the self-similar scaling properties of the activity time check out in practice.
Original languageEnglish
Pages (from-to)1047-1059
Number of pages12
JournalJournal of the Korean Mathematical Society
Issue number5
Publication statusPublished - 2001


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