Financial Section Overview

This web space is devoted to a novel approach to the analysis of financial data.  The underlying idea is that much of the behavior of financial markets can be described by heavy-tailed statistical distributions.  We do not make the assumption that the descriptive distribution is stationary.  Stable distributions are used as a tool for modeling data and the scale parameter of a stable distribution is used to estimate volatility of returns.  All of the analysis is based on the distribution of logarithmic returns -- differences in logarithms of prices.

The site map below shows suggested pathways through the material.  Each page or set of pages below contains a link to the next logical section as well as a link back to this page.  The map is designed so that you can easily jump around; if something seems too difficult at first, move to another set of pages.  The path starting with "Returns" starts very simply and hopefully somewhat intuitively leads into the sections that require some feeling for statistical distributions.  For users with some background in statistics a reasonable starting point might be "Fitting Market Data."  The path starting with "Stable Distributions" presents some basic information about stable distributions.  If you get lost, there is an index to all the pages.  Occasionally you will run into an "Under Construction" page where something is not yet ready; we will also use the "Under Construction" page to point to something that is new and not yet in the main pathway system. The link "Statistics FFT" shows how to use the fast Fourier transform to calculate statistical probability densities from characteristic functions.

Our research has led to a new set of distributions, the lognormal - stable and lognormal - normal.  These are mixture distributions.  The lognormal - normal (LNN) gives fits superior to the stable model for many market returns over long time frames.  Use the links: "LognormalStable" and "LognormalNormal."

As the site has grown to more than 70 pages, the thread of a theory of markets that is evolving is hard to follow.  A working paper, "Market Theory," hopefully helps to pull this back together.  The paper has links back to the site and is available in a printable pdf format.

Here is a link to our presentation at the Extreme Value Analysis Conference in Fort Collins, Colorado June 23-26, 2009.

We are developing an interactive site where you may try a variety of calculations on different securities or even submit your own data for stable analysis.  These routines are driven by webMathematica and are located on another server.  The site is still experimental and may not always be operating.  Your feedback will help us decide whether to continue the effort.

New
A power tail model for market returns with a double Pareto distribution.