A Multifractal Model of Asset Returns

Mandelbrot, Benoit B., Fisher, Adlai J. and Calvet, Laurent E., "A Multifractal Model of Asset Returns" (September 15, 1997). Cowles Foundation Discussion Paper No. 1164.

Abstract:

This paper presents the "multifractal model of asset returns" ("MMAR"), 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. First, the MMAR contains long-tails, as in Mandelbrot (1963), which focused on Levy-stable distributions. In contrast to Mandelbrot (1963), this model does not necessarily imply infinite variance. Second, the model contains long-dependence, the characteristic feature of fractional Brownian Motion (FBM), introduced by Mandelbrot and van Ness (1968). In contrast to FBM, the multifractal model displays long dependence in the absolute value of price increments, while price increments themselves can be uncorrelated. As such, the MMAR is an alternative to ARCH-type representations that have been the focus of empirical research on the distribution of prices for the past fifteen years. The distinguishing feature of the multifractal model is multiscaling of the return distribution's moments under time-rescalings. We define multiscaling, show how to generate processes with this property, and discuss how these processes differ from the standard processes of continuous-time finance. The multifractal model implies certain empirical regularities, which are investigated in a companion paper.

Facts on IBM Software

WebSphere MQ (known as MQSeries until 2002) is IBM's Message Oriented Middleware offering.

Lotus began its diversification from the desktop software business with its 1984 strategic founding investment in Ray Ozzie's Iris Associates, the creator of its Lotus Notes groupware platform. As a result of this early speculative move, Lotus had gained significant experience in network-based communications years before other competitors in the PC world had even started thinking about the Internet. Lotus initially brought Notes to market in 1989, and later reinforced its market presence with the acquisition of cc:Mail in 1991. In 1994, Lotus acquired Iris Associates. Lotus's dominant groupware position soon faced stiff competition from Microsoft Exchange, but in 2004, twenty years after its groundbreaking agreement with Iris, Lotus Notes continued to lead the market according to some measures.

With Rational, IBM now will provide a complete software development environment for companies that want to integrate their business processes and software infrastructure across their companies and with suppliers, customers and employees. This requires the integration of data management, systems management, collaboration, transaction and business process integration middleware and software development. The acquisition of Rational will strengthen IBM’s leadership in each of these segments, including software development, and reinforces IBM's commitment to open industry standards. The acquisition is an important element of IBM's e-business on demand strategy.

This site is growing and will contain info on subjects like domino extrafax lotus, weblogic websphere and uml examples.