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Skew Lognormal Cascade DistributionStephen Lihn / research archive

Quantitative finance
2008 to 2026

Data atlas / stock index

Nasdaq Index Daily Log Return

Thirty eight years of Nasdaq index data fit well with eta near 0.6.

Kurtosis 10 to 201971 to 2009Eta near 0.6
Nasdaq Index daily log return with a skew lognormal cascade fit.
The Nasdaq daily fit over 38 years.

Thirty eight years of Nasdaq index data fit well with eta near 0.6. The tail mass is clear in both directions, with the negative side the more important risk for a long position.

Data source: Yahoo Finance.

Related fits

Compare the shape.

Dow Daily Log Return for 80 YearsStock index / 1928 to 2008Russell 2000 Daily Log ReturnStock index / 1988 to 2008

Source shelf

Data and further reading

12 entries
  1. Yahoo FinanceMarket data and historical quotes used for several series.
  2. Nasdaq CompositeOfficial index information for the Nasdaq Composite.
  3. Federal Reserve Economic DataEconomic time series from the Federal Reserve Bank of St. Louis.
  4. Lihn 2008 on SSRNThe 2008 working paper on the scale invariant Brownian motion model.
  5. Lihn 2009 on SSRNThe working paper on higher order lognormal cascade distributions.
  6. Clark 1973Subordinated stochastic process model for speculative prices.
  7. Fernholz 2002Stochastic portfolio theory and the diversity index.
  8. Heavy tailed distributionsA reference overview of distributions with heavy tails.
  9. Lognormal distributionDefinition and properties of the lognormal distribution.
  10. Mandelbrot 1963The variation of certain speculative prices.
  11. Fat tailed distributionsA reference overview of heavy tailed probability distributions.
  12. Stochastic portfolio theoryA reference overview of stochastic portfolio theory.