英文标题：
《Inverse Gaussian quadrature and finite normal-mixture approximation of
the generalized hyperbolic distribution》
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作者：
Jaehyuk Choi, Yeda Du, Qingshuo Song
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最新提交年份：
2020
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英文摘要：
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. The proposed quadrature is not Gaussian, but it exactly integrates the polynomials of both positive and negative orders. Using the quadrature, the generalized hyperbolic distribution is efficiently approximated as a finite normal variance-mean mixture. Therefore, the expectations under the distribution, such as cumulative distribution function and European option price, are accurately computed as weighted sums of those under normal distributions. The generalized hyperbolic random variates are also sampled in a straightforward manner. The accuracy of the methods is illustrated with numerical examples.
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中文摘要：
在本研究中，利用高斯-厄米特求积与正态分布的关系，从高斯-厄米特求积中导出了广义逆高斯分布的数值求积。所提出的求积不是高斯的，而是正、负阶多项式的精确积分。利用求积，将广义双曲分布有效地近似为有限正态方差-均值混合分布。因此，该分布下的期望值，如累积分布函数和欧式期权价格，准确地计算为正态分布下的期望值的加权和。广义双曲随机变量也以简单的方式采样。数值算例说明了方法的准确性。
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分类信息：

一级分类：Statistics 统计学
二级分类：Computation 计算
分类描述：Algorithms, Simulation, Visualization
算法、模拟、可视化
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一级分类：Quantitative Finance 数量金融学
二级分类：Computational Finance 计算金融学
分类描述：Computational methods, including Monte Carlo, PDE, lattice and other numerical methods with applications to financial modeling
计算方法，包括蒙特卡罗，偏微分方程，格子和其他数值方法，并应用于金融建模
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一级分类：Quantitative Finance 数量金融学
二级分类：Pricing of Securities 证券定价
分类描述：Valuation and hedging of financial securities, their derivatives, and structured products
金融证券及其衍生产品和结构化产品的估值和套期保值
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