This article describes a versatile family of functions that are increasingly roughened by successive interpolations. They reproduce, in the simplest way possible, the main features of financial prices: continually varying volatility, discontinuity or concentration, and the fact that many changes...

This is a direct continuation of the preceding paper, with which it shares the front material and the numbering of the sections. A little repetition makes it possible to read this paper, part II, by itself. It describes the progression of the formalism from the financial model the author...

We showed in an earlier paper (1995a) that negatively correlated fractional Brownian motion (FBM) can be generated as a fractal sum of one kind of micropulses (FSM). That is, FBM of exponent is the limit (in the sense of finite-dimensional distributions) of a certain sequence of processes...

We begin with stochastic processes obtained as sums of "up-and-down" pulses with random moments of birth [tau] and random lifetime w determined by a Poisson random measure. When the pulse amplitude [var epsilon] -- 0, while the pulse density [delta] increases to infinity, one obtains a process...

The Multifractal Model of Asset Returns (See lt;a HREF=http://papers.ssrn.com/paper.taf?abstract_id=78588gt;Mandelbrot, Fisher, and Calvet, 1997lt;/Agt; ) proposes a class of multifractal processes for the modelling of financial returns. In that paper, multifractal processes are defined by a...

This paper presents the first empirical investigation of the Multifractal Model of Asset Returns (quot;MMARquot;). The MMAR, developed in Mandelbrot, Fisher, and Calvet (1997) (See Mandelbrot, Fisher, and Calvet, 1997 at the following URL: http://papers.ssrn.com/paper.taf?abstract_id=78588 ), is...

This paper presents the quot;multifractal model of asset returnsquot; (quot;MMARquot;), based upon the pioneering research into multifractal measures by Mandelbrot (1972, 1974). The multifractal model incorporates two elements of Mandelbrot's past research that are now well known in finance....

Having been crafted to welcome a new scientific journal, this paper looks forward but requires no special prerequisite. The argument builds on a technical wrinkle (used earlier but explained here fully for the first time), namely, the author’s grid-bound variant of Brownian motion B(t). While...

This article describes a versatile family of functions increasingly roughened by successive interpolations. They provide models of the variation of financial prices. More importantly, they are helpful "cartoons" of Brownian motions in multifractal time, BMMT, which are better models described in...