Inverse Gaussian quadrature and finite normal-mixture approximation of generalized hyperbolic distribution
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In this study, a numerical quadrature for the generalized inverse Gaussian distribution is derived from the Gauss--Hermite quadrature by exploiting its relationship with the normal distribution. Unlike Gaussian quadrature, the proposed quadrature exactly evaluates both positive and negative moments, thus improving evaluation accuracy. The generalized hyperbolic distribution is efficiently approximated as a finite normal variance-mean mixture with the quadrature. Therefore, the expectations under the distribution, such as cumulative distribution function and option price, are accurately computed as weighted sums of those under normal distributions.
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