Comparing Azzalini, Hansen, and Fernandez–Steel Skew-t Distributions

Summary

The document compares three ways to represent a skewed Student-t distribution in financial modeling: the Azzalini, Hansen, and Fernandez–Steel variants. It raises the practical question of whether one is better suited to financial data and notes that Hansen’s version is commonly used in finance, while the author has experience with Azzalini’s variant.

The only specific distinction offered is that Fernandez–Steel’s location and scale parameters may not directly represent the distribution’s mean and standard deviation. The text therefore presents Hansen’s parameterization as potentially more convenient, while describing it as slower than Fernandez–Steel because it requires additional calculations. It provides no comparative fit results, mathematical details, or evidence that establishes one variant as generally superior. Selection should depend on the model’s parameter interpretation, computational needs, and empirical fit to the data at hand.

Key ideas

• Three common skew-t parameterizations are Azzalini, Hansen, and Fernandez–Steel.
• The document reports that Hansen’s variant is commonly used in finance.
• Fernandez–Steel location and scale parameters may not equal the distribution’s mean and standard deviation.
• The document characterizes Hansen’s variant as more computationally involved than Fernandez–Steel.
• No empirical comparison is provided to establish which variant fits financial data best.

Tags

# Skew Student T variants: Azzalini vs Hansen vs Fernandez-Steel


# Skew Student T variants: Azzalini vs Hansen vs Fernandez-Steel












There are 3 common ways to represent Skew Student T Distribution: Azzalini, Hansen, Fernandez-Steel.

Are they equally good (flexible?) to represent financial data? I use Azzalini 2014 variant, but discovered recently that in finance Hansen variant used mostly.

Why? Is there some properties of Hansen that make it more suited to finance than Azzalini or Fernandez-Steel?

UPDATE:

It seems:



- Fernandez-Steel: $SkewT(loc, scale, \nu, \lambda)$ loc and scale are not interpretable numbers and aren't equal to $\mu, \sigma$.



So, Hansen seems to be most convenient variant, but slower than Fernandez-Steel because of additional computations.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.