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Skew Lognormal Cascade DistributionStephen Lihn / research archive

Quantitative finance
2008 to 2026

Data atlas / currency

Swiss Franc Against the US Dollar

A stable currency with a very good fit. Eta is small, but still far from zero.

Kurtosis 2 to 51975 to 2008Stable currency
Swiss franc against the US dollar daily log return with a skew lognormal cascade fit.
The Swiss franc fit from 1975 to 2008.

The fit is very good for this stable currency. Eta is small, but it is still far from zero. Even a reserve currency that moves less than an equity index keeps measurable tail risk.

Data source: Yahoo Finance.

Related fits

Compare the shape.

Japanese Yen Against the US DollarCurrency / 1975 to 2008Dow Daily Log Return for 80 YearsStock index / 1928 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.