论文标题
在两个因子的船体白色模型下定价百慕丹交换具有快速高斯转换
Pricing Bermudan Swaption under Two Factor Hull-White Model with Fast Gauss Transform
论文作者
论文摘要
本文介绍了一种快速，稳定的算法，用于评估两个因子赫尔 - 白模型下的百慕大交换。我们将数值集成评估百慕大交换的预期值的计算离散，而高斯内核和出现在其中。快速高斯变换可以应用于这些高斯内核总和，并将计算复杂度从$ O（n^2）$降低到$ o（n）$作为数值集成的网格点$ n $。我们还建议通过引入网格旋转来稳定相关性接近$ -1 $的情况。使用实际市场数据的数值实验表明，与没有快速高斯转换的方法相比，我们的方法显着减少了计算时间。他们还表明，在相关性接近$ -1 $且时间步长的情况下，网格旋转方法有助于计算稳定性。
This paper describes a fast and stable algorithm for evaluating Bermudan swaption under the two factor Hull-White model. We discretize the calculation of the expected value in the evaluation of Bermudan swaption by numerical integration, and Gaussian kernel sums appears in it. The fast Gauss transform can be applied to these Gaussian kernel sums, and it reduces computational complexity from $O(N^2)$ to $O(N)$ as grid points number $N$ of numerical integration. We also propose to stabilize the computation under the condition that the correlation is close to $-1$ by introducing the grid rotation. Numerical experiments using actual market data show that our method reduces the computation time significantly compared to the method without the fast Gauss transform. They also show that the method of the grid rotation contributes to computational stability in the situations where the correlation is close to $-1$ and time step is short.
