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Skew Lognormal Cascade DistributionStephen Lihn / research archive

Quantitative finance
2008 to 2026

Data atlas / currency

Japanese Yen Against the US Dollar

Thirty years of currency data, a very nice fit and a much lower eta than the Dow.

Kurtosis 2 to 51975 to 2008Lower eta
Japanese yen against the US dollar daily log return with a skew lognormal cascade fit.
The Japanese yen currency fit over 30 years.

The fit is very good for this currency. Eta is a lot less than for the Dow. The distribution still has visible fat tails, which is the central point of the archive.

Data source: Yahoo Finance.

Related fits

Compare the shape.

Swiss Franc Against the US DollarCurrency / 1975 to 200810 Year Treasury Daily Log ReturnBond / 1962 to 2008

Source shelf

Data and further reading

12 entries
  1. Yahoo FinanceMarket data and historical quotes used for several series.
  2. Federal Reserve Economic DataEconomic time series from the Federal Reserve Bank of St. Louis.
  3. US TreasuryDaily Treasury yield curve and interest rate data.
  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. Ornstein Uhlenbeck processA reference overview of the mean reverting process.
  9. Stable distributionBackground on stable distributions and heavy tails.
  10. Lognormal distributionDefinition and properties of the lognormal distribution.
  11. Mandelbrot 1963The variation of certain speculative prices.
  12. Stochastic portfolio theoryA reference overview of stochastic portfolio theory.