Generalized Hyperbolic and Inverse Gaussian Distributions: Limiting Cases and Approximation of Processes

By Ernst Eberlein, E. A. V. Hammerstein. 2003

163 citations recorded by the source corpus.

Subfields: Economics and Econometrics, Finance

View Paper: https://www.semanticscholar.org/paper/b15e761a8b043e82683a023ab3faec10b35e392d

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Economics and Econometrics

1. Antonis Papapantoleon
2. Murad S. Taqqu
3. Mark S. Veillette
4. Jan Kallsen
5. Jörn Kristen
6. Robert E. Gaunt
7. Ernst Eberlein
8. David Bolin

In Finance

1. Antonis Papapantoleon
2. Ernst Eberlein
3. Murad S. Taqqu
4. Mark S. Veillette
5. Jan Kallsen
6. Jörn Kristen
7. Robert E. Gaunt
8. Ole E. Barndorff-Nielsen

Citations in the corpus

• The Variance-Gamma Distribution: A Review (2023, unknown): “Like the VG distribution, GH distributions are widely used in financial modelling; see for example, Bibby and Sørensen [15], Eberlein and Keller [26] and Eberlein and Prause [27].”
• An introduction to Lévy processes with applications in finance (2008, background): “The GH distribution contains as special or limiting cases several known distributions, including the normal, exponential, gamma, variance gamma, hyperbolic and normal inverse Gaussian distributions; we refer to [29] for an exhaustive survey.”
• Numerical Computation of First-Passage Times of Increasing Lévy Processes (2009, methodology): “The Lévy-Khintchine representation given in [11] is not in the form (2) and some computation is needed to bring it into this form.”
• Risk management based on stochastic volatility (2003, methodology): “We note that many of the standard distributions used in statistics, such as Student t, Cauchy, variance gamma, normal inverse Gaussian, and the normal distribution are either special or limiting cases of the underlying class of distributions (cf. Eberlein and von Hammerstein (2002)).”
• Variance-Gamma approximation via Stein's method (2013, background): “The Variance-Gamma distributions have moments of arbitrary order (see Eberlein and Hammerstein [15]), in particular the mean and variance (for both parametrisations) of a random variable X with a Variance-Gamma distribution are given by”
• Geostatistical Modelling Using Non‐Gaussian Matérn Fields (2015, background): “The most well-known subclass of the type G Lévy process is the class of GH processes generated by the GH distribution (Barndorff-Nielsen, 1978; Eberlein & von Hammerstein, 2004).”