Skip to content
All library documents

Checking Whether an Asymmetric Laplace Model Has Finite Variance

Article Quant Q&A · Author: Anon9001
Read the original

Summary

The document describes a question about fitting an Asymmetric Laplace Distribution (ALD) to daily NIFTY 50 log returns and determining whether the fitted distribution has finite variance. The post gives fitted location, scale, and asymmetry parameters and raises confusion prompted by information about the related log-Laplace distribution, whose moments can depend on its parameters.

The author then reports finding a variance formula for the ALD and plugging in the stated asymmetry and scale values. The resulting calculation is taken as evidence that the fitted ALD has finite variance. The exchange provides no derivation of the formula or independent check of the numerical result, and the initial confusion concerns two related but distinct distributions. Readers should verify that the formula’s parameterization matches the fitted model before relying on the conclusion or applying it to return-risk estimates.

Key ideas

  • The question concerns whether an ALD fitted to index returns has finite variance.
  • The post gives fitted location, scale, and asymmetry parameters for the return distribution.
  • The author uses the ALD variance formula and concludes that the fitted variance is finite.
  • The response does not derive or independently validate the formula or calculation.
  • Confirm the distribution and parameterization before interpreting the variance result.

Tags

StatisticsEquitiesRisk management
Full text
# How to find out if Asymmetric Laplace Distribution is having Finite/Infinite Variance?


# How to find out if Asymmetric Laplace Distribution is having Finite/Infinite Variance?












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,

Anon9001.

## Answer by Anon9001 (score 1)

https://quant.stackexchange.com/a/74600

Forgot to check the Wiki page of the ALD Distribution as the Variance Formula of the ALD is there. K is the Asymmetry Parameter and Lamda is the Scale Parameter. Considering the values for the two are 1.0565 and 0.74% respectively the Variance of this Distribution is equal to 36682.89253 which I believe indicates the Variance of the ALD Distribution with these parameters is Finite.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

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