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Skew Lognormal Cascade DistributionStephen Lihn / research archive

Quantitative finance
2008 to 2026

Data atlas / commodity

XAU Index Daily Log Return

Impressive tails, a lower eta than the Dow and little skew.

Kurtosis 5 to 101983 to 2008Little skew
XAU Index daily log return with a skew lognormal cascade fit.
The PHLX Gold and Silver Sector Index fit.

XAU has impressive tails, but eta is smaller than the Dow. It does not have large skewness either. The index offers a useful contrast with gold bullion, where positive skew is strong.

Data source: PHLX Gold and Silver Sector Index, via Yahoo Finance.

Related fits

Compare the shape.

Gold Against the US DollarCommodity / 1972 to 2009VIX Daily Log ReturnVolatility / 1990 to 2008

Source shelf

Data and further reading

12 entries
  1. LBMA precious metal pricesLondon benchmark prices and market data.
  2. World Gold Council dataGold price data and market research.
  3. Cboe GVZThe Cboe dashboard for the gold volatility index.
  4. Federal Reserve Economic DataEconomic time series from the Federal Reserve Bank of St. Louis.
  5. Lihn 2008 on SSRNThe 2008 working paper on the scale invariant Brownian motion model.
  6. Lihn 2009 on SSRNThe working paper on higher order lognormal cascade distributions.
  7. Clark 1973Subordinated stochastic process model for speculative prices.
  8. Fat tailed distributionsA reference overview of heavy tailed probability distributions.
  9. Lognormal distributionDefinition and properties of the lognormal distribution.
  10. Mandelbrot 1963The variation of certain speculative prices.
  11. Heavy tailed distributionsA reference overview of distributions with heavy tails.
  12. Stochastic portfolio theoryA reference overview of stochastic portfolio theory.