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Skew Lognormal Cascade DistributionStephen Lihn / research archive

Quantitative finance
2008 to 2026

Software / GNU Octave

Implementation

The distribution was prototyped in GNU Octave. These notes preserve the release history, installation steps and tests that accompanied the original package.

GNU OctaveRelease historyPersonal and educational use

I implemented the numerical calculation routines in GNU Octave. You can use the code freely for personal and educational purposes. Please contact me for commercial use.

Release archiveThe original server no longer serves the historical ZIP files. The release history and file names are retained below for reference. Contact the author for access to the current package.

Release history

VersionDateFile nameStatus
v1.2February 7, 2010skew_lognormal_cascade_dist_octave_1.2.zipArchive unavailable
v1.1February 1, 2009skew_lognormal_cascade_dist_octave_1.1.zipArchive unavailable
v1.0December 31, 2008skew_lognormal_cascade_dist_octave_1.0.zipArchive unavailable

Installation

Unzip the package, then copy the .m files into your Octave working directory. The routines use the analytic structure set out in the 2008 analytic paper.

Tests

Run slog_dist_test1.m to watch a plot of the probability density function. Edit the parameters eta, beta and growth in the file to see how the distribution evolves.

The file slog_solve_zp_test.m has more detail about the inner structure of the integrand that leads to the density. The data atlas shows the fitted shapes these parameters produce.

Comments and feedback

Email Stephen Lihn at stevelihn a t gmail d o t com. I would like to hear what you think, good or bad.

Continue

Run the browser simulatorChange the parameters and inspect the density.Read the N^3/2 lawThe scaling argument behind the market model.

Source shelf

Data and further reading

11 entries
  1. GNU OctaveThe GNU Octave scientific programming environment.
  2. Octave projectThe Octave numerical computing project.
  3. Octave packagesAdditional packages for GNU Octave.
  4. MaximaThe Maxima computer algebra system.
  5. GNU General Public LicenseThe license used by GNU Octave and related tools.
  6. Lihn 2008 on SSRNThe 2008 working paper on the scale invariant Brownian motion model.
  7. Lihn 2009 on SSRNThe working paper on higher order lognormal cascade distributions.
  8. Clark 1973Subordinated stochastic process model for speculative prices.
  9. Fernholz 2002Stochastic portfolio theory and the diversity index.
  10. Lognormal distributionDefinition and properties of the lognormal distribution.
  11. Fat tailed distributionsA reference overview of heavy tailed probability distributions.