Exercise

KDE of a loss distribution

Kernel density estimation (KDE) can fit distributions with 'fat tails', i.e. distributions with occasionally large deviations from the mean (such as the distribution of portfolio losses).

In Chapter 2 you learned about the Student's T distribution, which for low degrees of freedom can also capture this feature of portfolio losses.

You'll compare a Gaussian KDE with a T distribution, each fitted to provided portfolio losses from 2008 - 2009. You'll visualize the relative fits of each using a histogram. (Recall the T distribution uses fitted parameters params, while the gaussian_kde, being non-parametric, returns a function.)

The function gaussian_kde() is available, as is the t distribution, both from scipy.stats. Plots may be added to the provided axis object.

Instructions

100 XP
  • Fit a t distribution to portfolio losses.
  • Fit a Gaussian KDE to losses by using gaussian_kde().
  • Plot the probability density functions (PDFs) of both estimates against losses, using the axis object.