Hyperbolic Distributions and Ramifications: Contributions to Theory and Application

Barndorff–Nielsen, Ole E.; Blæsild, P.

doi:10.1007/978-94-009-8549-0_2

Cited by 125 publications

(72 citation statements)

References 2 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This family of probability distributions was introduced in Barndorff-Nielson (1977, 1978 and further explored in Barndorff-Nielson and Blaesild (1981). See also McNeil et al (2005).…”

Section: The Skewed T Distributionsmentioning

confidence: 99%

Risk Forecasting with GARCH, Skewed t Distributions, and Multiple Timescales

Kercheval

Liu

2011

Handbook of Modeling High‐Frequency Data in Finance

View full text Add to dashboard Cite

“…This family of probability distributions was introduced in Barndorff-Nielson (1977, 1978 and further explored in Barndorff-Nielson and Blaesild (1981). See also McNeil et al (2005).…”

Section: The Skewed T Distributionsmentioning

confidence: 99%

Risk Forecasting with GARCH, Skewed t Distributions, and Multiple Timescales

Kercheval

Liu

2011

Handbook of Modeling High‐Frequency Data in Finance

View full text Add to dashboard Cite

“…In particular, we pursue an experiment to check the validation of the FastICA approach with Normal Inverse Gaussian (NIG) distributed ICs, where the NIG distribution is a subclass of the GH distribution with the fixed parameter λ = −0.5, see Barndorff-Nielsen and Blaesild (1981). We generate d = 50 NIG samples with T = 1000 observations, i.e.…”

Section: Simulation Studymentioning

confidence: 99%

Portfolio Value at Risk Based on Independent Components Analysis

2005

View full text Add to dashboard Cite

Risk management technology applied to high dimensional portfolios needs simple and fast methods for calculation of Value-at-Risk (VaR). The multivariate normal framework provides a simple off-the-shelf methodology but lacks the heavy tailed distributional properties that are observed in data. A principle component based method (tied closely to the elliptical structure of the distribution) is therefore expected to be unsatisfactory. Here we propose and analyze a technology that is based on Independent Component Analysis (ICA). We study the proposed ICVaR methodology in an extensive simulation study and apply it to a high dimensional portfolio situation. Our analysis yields very accurate VaRs.

show abstract

“…Some examples are Barndorff-Nielsen (1979), Barndorff-Nielsen and Blaesild (1981), Eberlein and Keller (1995), Prause (1999), Bibby and Sørensen (2003), Mencía and Sentana (2004) and .…”

Section: Introductionmentioning

confidence: 99%

“…The first four moments and skewness and kurtosis of the generalized hyperbolic (GH) distribution were given by Barndorff-Nielsen and Blaesild (1981). The expressions are complicated and the reference rather difficult to obtain.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Moments of the generalized hyperbolic distribution

et al. 2010

View full text Add to dashboard Cite

In this paper we demonstrate a recursive method for obtaining the moments of the generalized hyperbolic distribution. The method is readily programmable for numerical evaluation of moments. For low order moments we also give an alternative derivation of the moments of the generalized hyperbolic distribution. The expressions given for these moments may be used to obtain moments for special cases such as the hyperbolic and normal inverse Gaussian distributions. Moments for limiting cases such as the skew hyperbolic t and variance gamma distributions can be found using the same approach.

show abstract

Hyperbolic Distributions and Ramifications: Contributions to Theory and Application

Cited by 125 publications

References 2 publications

Risk Forecasting with GARCH, Skewed t Distributions, and Multiple Timescales

Risk Forecasting with GARCH, Skewed t Distributions, and Multiple Timescales

Portfolio Value at Risk Based on Independent Components Analysis

Moments of the generalized hyperbolic distribution

Contact Info

Product

Resources

About