The Meixner Process

This Demonstration shows a path of the (extended) Meixner process with four parameters and a cross-sectional ("marginal") density function of the process at a chosen moment in time. The kurtosis and skewness of the density at the given time are also displayed. The Meixner process is a pure-jump Lévy process with semi-heavy tails, which has been used successfully for stock price modelling and valuing derivative instruments. The Demonstration makes use of Mathematica 8's ability to generate random variates when an explicit formula for the probability density function is given.


  • [Snapshot]
  • [Snapshot]
  • [Snapshot]


The Meixner process is a three-parameter pure jump Lévy process that was introduced in [1] and applied to finance in [2]. As with other similar processes, one can add a "drift" parameter, creating a four-parameter process particularly convenient for pricing derivative instruments. The process originated in the theory of orthogonal polynomials. It is a pure jump Lévy process (i.e. it has no continuous component) and was defined by explicitly giving its density function, which plays the central role in this Demonstration.
[1] W. Schoutens and J. L. Teugels, "Lévy Processes, Polynomials and Martingales," Communications in Statistics: Stochastic Models, 14, 1998 pp. 335–349.
[2] W. Schoutens, Lévy Processes in Finance: Pricing Financial Derivatives, New York: John Wiley & Sons, 2003.
    • Share:

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.

Mathematica »
The #1 tool for creating Demonstrations
and anything technical.
Wolfram|Alpha »
Explore anything with the first
computational knowledge engine.
MathWorld »
The web's most extensive
mathematics resource.
Course Assistant Apps »
An app for every course—
right in the palm of your hand.
Wolfram Blog »
Read our views on math,
science, and technology.
Computable Document Format »
The format that makes Demonstrations
(and any information) easy to share and
interact with.
STEM Initiative »
Programs & resources for
educators, schools & students.
Computerbasedmath.org »
Join the initiative for modernizing
math education.
Step-by-Step Solutions »
Walk through homework problems one step at a time, with hints to help along the way.
Wolfram Problem Generator »
Unlimited random practice problems and answers with built-in step-by-step solutions. Practice online or make a printable study sheet.
Wolfram Language »
Knowledge-based programming for everyone.
Powered by Wolfram Mathematica © 2018 Wolfram Demonstrations Project & Contributors  |  Terms of Use  |  Privacy Policy  |  RSS Give us your feedback
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to Mathematica Player 7EX
I already have Mathematica Player or Mathematica 7+