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Skew Lognormal Cascade DistributionStephen Lihn / research archive

Quantitative finance
2008 to 2026

Data atlas / bond

10 Year Treasury Daily Log Return

A symmetric fit with eta around 0.5, far below the daily Dow series.

Kurtosis 2 to 51962 to 2008Eta near 0.5
10 year Treasury daily log return with a skew lognormal cascade fit.
The 10 year Treasury fit from 1962 to 2008.

The fit is good in the tails and very symmetric. The central probability is slightly underestimated. Eta is much less than the Dow and is around 0.5.

The symmetry is a useful contrast with equities and oil. Bonds can have fat tails without a strong directional skew.

Data source: US Treasury yield data.

Related fits

Compare the shape.

VIX Daily Log ReturnVolatility / 1990 to 2008Japanese Yen Against the US DollarCurrency / 1975 to 2008

Source shelf

Data and further reading

12 entries
  1. US TreasuryDaily Treasury yield curve and interest rate data.
  2. Federal Reserve Economic DataEconomic time series from the Federal Reserve Bank of St. Louis.
  3. Yahoo FinanceMarket data and historical quotes used for several series.
  4. Nasdaq CompositeOfficial index information for the Nasdaq Composite.
  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. Fernholz 2002Stochastic portfolio theory and the diversity index.
  9. Ornstein Uhlenbeck processA reference overview of the mean reverting process.
  10. Stable distributionBackground on stable distributions and heavy tails.
  11. Lognormal distributionDefinition and properties of the lognormal distribution.
  12. Stochastic portfolio theoryA reference overview of stochastic portfolio theory.