Processes of normal inverse Gaussian type

By Ole E. Barndorff-Nielsen. 1997

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Diffusion-type models with given marginal distribution and autocorrelation function (2005, methodology): “The construction considered in this section is closely related to the sums of Ornstein-Uhlenbeck processes driven by Lévy processes introduced in Barndorff-Nielsen, Jensen & Sørensen (1998). Our aim is to construct a stationary process X with a given marginal density f and with autocorrelation funct”
Variance-Optimal Hedging for Processes with Stationary Independent Increments (2006, background): “The Annals of Applied Probability 2006, Vol. 16, No. 2, 853–885 DOI: 10.1214/105051606000000178 © Institute of Mathematical Statistics, 2006”
A comparison of volatility models: Does anything beat a GARCH(1,1) ? (2001, methodology): “By using intra-day returns to calculate a measure for the time-varying volatility, Andersen and Bollerslev (1998a) established that volatility models do provide good forecasts of the conditional variance. In this paper, we take the same approach and use intra-day estimated measures of volatility to ”
Maximum likelihood estimation in processes of Ornstein-Uhlenbeck type (2009, methodology): “In this context, our work is related with the one of Barndorff-Nielsen (1988) who proposes a simulationbased likelihood approximation method when D is an inverse Gaussian or a normal inverse Gaussian distribution.”
Sato processes and the valuation of structured products (2009, methodology): “1998 ), the Normal Inverse Gaussian (NIG) (Barndorff-Nielsen 1998 ), and the Meixner (MXNR) process (Schoutens 2002 , 2003 ) reported by Carr et al.”
Lévy Processes in Finance: Inverse Problems and Dependence Modelling (2004, background): “Cependant, dans le contexte de processus avec sauts, bien que plusieurs articles proposent des modèles paramétriques à base de processus de Lévy [5, 22, 36, 62, 67, 71], il n’existait pas, avant cet étude, de méthode permettant d’en choisir un parmi cette multitude de modèles ni d’algorithme stable ”
Convergence of a discretization scheme for jump-diffusion processes with state–dependent intensities (2004, methodology): “Specific models of this type (in which the Brownian component is dropped altogether) have been developed by Barndorff-Nielsen (1998) and Madan & Seneta (1990).”
Spread Option Valuation and the Fast Fourier Transform (2002, methodology): “This includes the Variance Gamma (VG) model [15], the inverse Gaussian model [3] and numerous stochastic volatility and stochastic interest rates models in the general affine jump-diffusion family [1, 4, 6, 14, 21].”
Risk management based on stochastic volatility (2003, methodology): “(1998), Keller (1997), Barndorff-Nielsen (1998), Eberlein (2001), Eberlein and Prause (2002)) the initial model was pushed further. It can be handled now on the level of generalized hyperbolic Lévy motions. We note that many of the standard distributions used in statistics, such as Student t, Cauchy”
Optimal Portfolios with Bounded Capital at Risk (2001, methodology): “Various models have been suggested: a simple hyperbolic model has been investigated by Bibby and Sørensen (1997); a more general class of models has been suggested by Barndorff-Nielsen (1998).”
Realised power variation and stochastic volatility models (2003, background): “Drawn is σ [2] n and σ [ 1 ] n against time, together with their associate realised power variation estimators.”
Local asymptotic normality for normal inverse Gaussian Lévy processes with high-frequency sampling (2010, methodology): “One can consult Barndorff–Nielsen [6,7] for more analytical facts concerning the NIG distribution and the NIG Lévy process.”