# Fitting the Meixner Distribution to S&P 500 Returns

Fitting the Meixner Distribution to S&P 500 Returns

The Meixner process is a Lévy pure jump stochastic process that was introduced into mathematical finance in 2001 by Schoutens. Schoutens showed that the normal distribution provides a very poor fit to the log returns of the S&P 500 index for the years 1970–2001 but that the Meixner distribution (for suitably chosen parameters) provides an excellent fit. In this Demonstration we confirm this and show that, although the parameters found by Schoutens no longer provide as good a fit to the prices for the period 2001–2010, one can use Mathematica to obtain new parameters that provide almost as good a fit to the latter data as Schoutens' values to the earlier ones.

The initial setting shows (in red) the Meixner process fitted to the S&P 500 index (green) using Schoutens' parameters. The fit is almost perfect. To the left of the graph the distance in variation between the two distributions is shown. Choosing the period 2001–2010 from the setter bar shows that Schouten's fit is no longer as good for this decade. However, choosing the "best 2001–2010" bookmark displays a nearly-as-good fit for the later period, using new values of the parameters.