Heston-Hull-White PDE的ADI有限差分格式
ADI finite difference schemes for the Heston-Hull-White PDE
AI总结：
本文研究交替方向隐式(ADI)时间离散格式在三维Heston-Hull-White偏微分方程数值求解中的有效性，通过非均匀空间网格上的有限差分半离散化，验证了ADI格式在多种情形下的稳定性、精度和效率。
摘要：
本文研究了交替方向隐式(ADI)时间离散格式在三维Heston-Hull-White偏微分方程数值求解中的有效性，该方程通过非均匀空间网格上的有限差分格式进行半离散化。我们考虑了具有任意相关系数、时变均值回归水平、短期和长期到期日的Heston-Hull-White模型，以及满足和不满足Feller条件的情况。此外，还考虑了欧式看涨期权和向上敲出看涨期权。通过大量测试表明，ADI格式在参数选择适当的情况下，在稳定性、精度和效率方面在所有情形下均表现良好。
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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