The NIG-S&ARCH model: a fat-tailed, stochastic, and autoregressive conditional heteroskedastic volatility model

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Value at Risk with time varying variance, skewness and kurtosis--the NIG-ACD model (2009, unknown): “2 The NIGS&ARCH model of Jensen and Lunde (2001) is given by (3) and (4) meaning that the steepness and asymmetry of the NIG distribution is forced to be constant in their specication.”
American Option Pricing Using GARCH Models and the Normal Inverse Gaussian Distribution (2008, unknown): “Following Jensen & Lunde (2001) the NIG (μ, δ, a, b) distribution can be defined in terms of the so called location and scale invariant parameters as fNIG (x;μ, δ, a, b) = a πδ exp µp a2 − b2 + b(x− μ) δ ¶ q µ x− μ δ ¶−1 K1 µ aq µ x− μ δ ¶¶ , (7) where q (z) = √ 1 + z2 and K1 (·) is the modified…”
The Generalized Hyperbolic Skew Student’s t-Distribution (2006, methodology): “For these reasons, it has been used repeatedly for financial applications, both as the conditional distribution of a GARCH-model (Andersson, 2001; Jensen and Lunde, 2001; Forsberg and Bollerslev, 2002; Venter and de Jongh, 2002) and as the unconditional †Address for correspondence: The Norwegian…”