Generalized Hyperbolic Models

Eberlein, Ernst

doi:10.1002/9780470061602.eqf08023

Cited by 6 publications

(3 citation statements)

References 8 publications

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“…The alternative approach of starting from g T and F X and constructing V via (6) can lead to v-transforms that are cumbersome and computationally expensive to evaluate. For example, for applications to asset return modelling, we might choose a marginal model from the generalized hyperbolic family (Barndorff-Nielsen, 1978;Barndorff-Nielsen and Blaesild, 1981;Eberlein, 2010). In this case the inversion of the cumulative distribution function requires numerical integration of the density and numerical root finding, which makes the evaluation of V in (6) very slow.…”

Section: Characterizing V-transformsmentioning

confidence: 99%

Modelling volatile time series with v-transforms and copulas

McNeil¹

2020

Preprint

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An approach to the modelling of financial return series using a class of uniformity-preserving transforms for uniform random variables is proposed. V-transforms describe the relationship between quantiles of the return distribution and quantiles of the distribution of a predictable volatility proxy variable constructed as a function of the return. V-transforms can be represented as copulas and permit the formulation and estimation of models that combine arbitrary marginal distributions with linear or non-linear time series models for the dynamics of the volatility proxy. The idea is illustrated using a transformed Gaussian ARMA process for volatility, yielding the class of VT-ARMA copula models. These can replicate many of the stylized facts of financial return series and facilitate the calculation of marginal and conditional characteristics of the model including quantile measures of risk. Estimation of models is carried out by adapting the exact maximum likelihood approach to the estimation of ARMA processes.

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Section: Characterizing V-transformsmentioning

confidence: 99%

Modelling volatile time series with v-transforms and copulas

McNeil¹

2020

Preprint

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“…We will apply Theorem 2 to the family of symmetric generalized hyperbolic (GH) distributions. This is a very popular family for modelling financial returns and there are many useful sources for the properties of these distributions including Barndorff-Nielsen (1978), Barndorff-Nielsen and Blaesild (1981), Eberlein (2010) and McNeil et al (2015).…”

Section: The Case Of Generalized Hyperbolic Distributionsmentioning

confidence: 99%

On the Basel Liquidity Formula for Elliptical Distributions

Balter

McNeil

2018

Risks

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A justification of the Basel liquidity formula for risk capital in the trading book is given under the assumption that market risk-factor changes form a Gaussian white noise process over 10-day time steps and changes to P&L are linear in the risk-factor changes. A generalization of the formula is derived under the more general assumption that risk-factor changes are multivariate elliptical. It is shown that the Basel formula tends to be conservative when the elliptical distributions are from the heavier-tailed generalized hyperbolic family. As a by-product of the analysis a Fourier approach to calculating expected shortfall for general symmetric loss distributions is developed.

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“…A class of multivariate skewed distributions that has received a lot of attention in the financial literature is the class of generalized hyperbolic (GH) distributions; see McNeil, Frey & Embrechts (2005) and Eberlein (2010). Let µ, κ ∈ R d denote the parameters of location and skewness, let Σ ∈ R d×d be a symmetric, positive-definite dispersion matrix and l et λ ∈ R, χ, ψ ∈ R + be scalars.…”

Section: Generalized Hyperbolic Distributionmentioning

confidence: 99%

On the computation of multivariate scenario sets for the skew-tand generalized hyperbolic families

Giorgi

McNeil

2016

Computational Statistics & Data Analysis

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We examine the problem of computing multivariate scenarios sets for skewed distributions. Our interest is motivated by the potential use of such sets in the stress testing of insurance companies and banks whose solvency is dependent on changes in a set of financial risk factors. We define multivariate scenario sets based on the notion of half-space depth (HD) and also introduce the notion of expectile depth (ED) where half-spaces are defined by expectiles rather than quantiles. We then use the HD and ED functions to define convex scenario sets that generalize the concepts of quantile and expectile to higher dimensions. In the case of elliptical distributions these sets coincide with the regions encompassed by the contours of the density function. In the context of multivariate skewed distributions, the equivalence of depth contours and density contours does not hold in general. We consider two parametric families that account for skewness and heavy tails: the generalized hyperbolic and the skewt distributions. By making use of a canonical form representation, where skewness is completely absorbed by one component, we show that the HD contours of these distributions are near-elliptical and, in the case of the skew-Cauchy distribution, we prove that the HD contours are exactly elliptical. We propose a measure of multivariate skewness as a deviation from angular symmetry and show that it can explain the quality of the elliptical approximation for the HD contours.

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Generalized Hyperbolic Models

Cited by 6 publications

References 8 publications

Modelling volatile time series with v-transforms and copulas

Modelling volatile time series with v-transforms and copulas

On the Basel Liquidity Formula for Elliptical Distributions

On the computation of multivariate scenario sets for the skew-tand generalized hyperbolic families

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