I was fitting the NIFTY 50 Daily Log Returns (To be more precise Returns in this case refers to the Log of 1+Returns rather than Log of Returns as Log cannot be taken of negative values which returns can be) from 2013-2023 to Asymmetric Laplace Distribution and I found the closest fit to the Empirical Distribution is the ALD with these parameters:
Location (µ) = 0.13%, Scale (b) = 0.74% and Asymmetry Parameter (k) = 1.0565.
I was wondering though whether the ALD with these parameters has Finite Variance or Infinite Variance as the Wiki article on the Log-Laplace Distribution is suggesting that depending on the parameters the Log-Laplace Distribution can be infinite/finite variance.
I read the paper linked in the article which referenced this issue but I can't seem to understand what the paper is suggesting. Here is a link to the paper (Kozubowski and Podgorsky: A Log Laplace Growth Rate Model, Mathematical Scientist, vol. 28, 2003) in case interested.
Thanks for all your help,