Approximation of Multiple Integrals over Hyperboloids with Application to a Quadratic Portfolio with Options
Jules Sadefo Kamdem, Alan Genz
我们考虑涉及金融二次期权组合的应用程序,当联合基础日志返回随着多变量椭圆分布而变化时。 这激发了对方法的需求,以近似多积分而不是双倍体。 转换用于将双倍体积分减少到两个径向积分和两个球面积体的产物。 构建了变换积分的数值近似方法。 这些方法的应用是用一些金融应用的例子来证明的。
We consider an application involving a financial quadratic portfolio of options, when the joint underlying log-returns changes with multivariate elliptic distribution. This motivates the needs for methods for the approximation of multiple integrals over hyperboloids. A transformation is used to reduce the hyperboloid integrals to a product of two radial integrals and two spherical surface integrals. Numerical approximation methods for the transformed integrals are constructed. The application of...