In the MathBox entry from 13 December, we showed the implied distribution of DAX returns when using the Cornish Fisher expansion.
As a rule of thumb, this works nicely as long as the excess kurtosis is smaller than 8. What happens if the implied distribution of returns is really fat-tailed?
![](https://www.mathconsult.co.at/wp-content/uploads/2019/07/eurchf.png)
The exchange rate of EUR and Swiss Franc between the years 2013 and 2017 showed an excess kurtosis of 590. The Cornish-Fisher transformation between the implied distribution of returns and the standard normal distribution is not bijective any more and leads to weird distributions.
![](https://www.mathconsult.co.at/wp-content/uploads/2019/07/CHFEUR8.png)
![](https://www.mathconsult.co.at/wp-content/uploads/2019/07/CHFEUR4.png)
![](https://www.mathconsult.co.at/wp-content/uploads/2019/07/CHFEUR0.png)