Statistical Modeling of Stock Returns: A Historical Survey with Some Methodological Reflections

This paper aims at identifying the motivating forces that gave birth to the statistical models of asset returns since the beginning of the twentieth century. The major question addressed is: Where do statistical models of asset returns come from?" This central question encompasses a number of secondary ones: What do these models do? Do they explain or simply describe the empirical regularities of asset returns, identified at different historical periods? If explanation provides `something', over and above description, then how can it be defined? Moreover, how is this reflected on explanatory versus descriptive models of asset returns? In the context of the models identified as explanatory, do these models offer an actual explanation for the regularities of interest or merely a potential explanation? Related to the last question, does the realism of the assumptions underlying the explanatory models matter? Has the literature adopted a realist or an instrumentalist attitude towards the explanatory models of asset returns? Our answers to these questions are being informed by our attempts to draw some analogies between the main issues concerning the statistical modelling of asset prices and those concerning the theoretical modelling of the Brownian motion in Physics.