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摘要翻译：
本文研究了交替方向隐式(ADI)时间离散格式在三维Heston-Hull-White偏微分方程数值解中的有效性。我们考虑了具有任意相关因子的Heston-Hull-White模型，具有时间相关的均值回复水平，具有较短和较长的成熟度，在满足Feller条件和不满足Feller条件的情况下，我们考虑了Heston-Hull-White模型。此外，欧式看涨期权和向上向外看涨期权均有考虑。通过广泛的测试表明，ADI方案在适当选择参数的情况下，在稳定性、精度和效率方面，在所有情况下都表现出色。
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英文标题：
《ADI finite difference schemes for the Heston-Hull-White PDE》
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作者：
Tinne Haentjens and Karel J. in 't Hout
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最新提交年份：
2011
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分类信息：
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：Mathematics 数学
二级分类：Numerical Analysis 数值分析
分类描述：Numerical algorithms for problems in analysis and algebra, scientific computation
分析和代数问题的数值算法，科学计算
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英文摘要：
In this paper we investigate the effectiveness of Alternating Direction Implicit (ADI) time discretization schemes in the numerical solution of the three-dimensional Heston-Hull-White partial differential equation, which is semidiscretized by applying finite difference schemes on nonuniform spatial grids. We consider the Heston-Hull-White model with arbitrary correlation factors, with time-dependent mean-reversion levels, with short and long maturities, for cases where the Feller condition is satisfied and for cases where it is not. In addition, both European-style call options and up-and-out call options are considered. It is shown through extensive tests that ADI schemes, with a proper choice of their parameters, perform very well in all situations - in terms of stability, accuracy and efficiency.
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PDF链接：
https://arxiv.org/pdf/1111.4087
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