Scaling in financial prices: I. Tails and dependence

The scaling properties of financial prices raise many questions. To provide background—appropriately so in the first issue of a new journal!—this paper, part I (sections 1 to 3), is largely a survey of the present form of some material that is well known yet repeatedly rediscovered. It originated in the author’s work during the 1960s. Part II follows as sections 4 to 6, but can to a large extent be read separately. It is more technical and includes important material on multifractals and the ‘star equation’; part of it appeared in 1974 but is little known or appreciated—for reasons that will be mentioned. Part II ends by showing the direct relevance to finance of a very recent improvement on the author’s original (1974) theory of multifractals.