正分裂法用于Hull & White二维Black-Scholes方程
Positive Splitting Method for the Hull & White 2D Black-Scholes Equation
AI总结：
本文提出一种局部一维分裂法求解Hull & White模型中带有混合导数项的二维Black-Scholes方程，通过拟合有限体积差分方案处理边界退化问题，保证非负性并验证了方法的有效性。
摘要：
本文提出了一种局部一维（LOD）分裂法，用于数值求解出现在Hull & White模型中的二维Black-Scholes方程，该模型用于定价具有随机波动率的欧式期权，其特征是存在混合导数项。该抛物型方程在x=0边界处退化，我们应用在[23]中提出的拟合有限体积差分方案以处理退化问题。证明了离散最大原理，因此我们的方法保持非负性。数值实验展示了差分方案的有效性。
英文摘要：
In this paper we present a locally one-dimensional (LOD) splitting method to solve numerically the two-dimensional Black-Scholes equation, arising in the Hull & White model for pricing European options with stochastic volatility, characterized by the presence of a mixed derivative term. The parabolic equation degenerates on the boundary x = 0 and we apply a fitted finite-volume difference scheme, proposed in [23], in order to resolve the degeneration. Discrete maximum principle is proved and therefore our method preserves the non-negativity. Numerical experiments illustrate the efficiency of our difference scheme.
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