在图9中,我们展示了各种算法的真实价格的卡尔曼估计。该图突出了KEM算法在存在跳跃时的缺点,即它过度平滑了跳跃附近的价格。5.4 GARCH(1,1)-跳跃模型的模拟数据除了跳跃差异模型之外,我们还评估了多元GARCH(1,1)-跳跃定价模型[15,31,8]的算法,其中跳跃的影响持续存在于价格波动中。使用G ARCH(1,1)跳跃模型,对数价格数据生成为Xi(t)=Xi(t)-1)+hiVi(t)+Ji(t)Zi(t)+Dhi(t+1)=bihi(t)+ai(Xi(t)-Xi(t)-1)-D) +cihi(0)=Γi,i其中ai,bi,ci是非负的,bi+ai<1,ci=Γi,i(1-人工智能-bi)。这里v(t)被建模为具有oVi(t)的多变量正态分布~ 1)1 N)1 N)1 N)1 N/1 1 1 N/1 1 1 N/1 1 1 N/1 1 1 1 N/1 1 1.2e-10 1.3 e-10 10 1.3 e-10 1.3 e-10 1.3 e-10 1.3 e-10 1.3 e-10 1.3 e-10 1.3 e-10 1.3 e-10 1.3 e-10 1.3 e-10 1.3 e-10 1.3 e-10 1.3 e-10 1.3 e-10 1.3 e-10 1.3 e-10 10 10 1.3 e-10 1.3 e-10 10 1.3 e-10 10 1.3 e-10 10 1.3 e-10 10 1.3 e-10 1.3 e-10 1 1 1.3 e-10 10 1 1.1.3 e-10 10 1 1.3 e-10 10 1.3 e-10 10 10 10 10 10 10 10 10 10 10 10 1 1.2.4e-10 2.3e-100.9995 0.00 01 3e-10 1.3e-10 1.2e-10 1.3e-10 7.9e-10 6e-100.9996.25e-06 2.4e-10 1.6e-10 1.6e-10 1.7e-10 4.7e-10 4.5e-100.999 2.5e-05 4.5e-10 1.7e-10 1.7e-10 1.8e-10 9.8e-10 6.9e-100.999 0.0001 8.2e-10 1.6e-10 1.7e-10 1.7e-10 1.7e-10 1.7e-09表2:跳跃模型的投资组合差异,最佳表现突出显示在绿色。2)vvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvv05 1.1 0.2 1 0.21 0.22 1.5 1.40.999 0.0001 4.8 0.20.2 0.21 4.6 3.6表3:跳跃模型的平均共变误差,最佳性能以绿色突出显示。
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