Traditionally, financial theory and in particular asset pricing models have
assumed (implicitly or explicitly) a certain probabilistic structure for s
peculative prices. The probabilistic structure is usually defined in terms
of specific statistical models and relates to the dependence, heterogeneity
and the distribution of such prices. The primary objective of this paper i
s to trace the development of various statistical models proposed since Bac
helier (1900), in an attempt to assess how well these models capture the em
pirical regularities exhibited by data on speculative prices.