论文标题
赫尔 - 白色模型中屏障选项的半关闭形式价格
Semi-closed form prices of barrier options in the Hull-White model
论文作者
论文摘要
在本文中，我们得出了hull-with模型的屏障（也许是时间依赖的）选项的半锁定形式，即，底层遵循时间依赖的OU过程，并带有均值回复的漂移。我们的方法与（Carr and Itkin，2020）中的方法相似，其中将广义积分转换的方法应用于时间依赖性OU模型中的定价障碍选项，但将其扩展到了无限域（这是尚未解决的问题）。另外，我们使用热电位方法来解决相同的问题。通过半闭合解决方案，我们的意思是，首先，我们需要在数值上求解第一类的线性伏特拉方程，然后将期权价格表示为一维积分。我们的分析表明，计算上我们的方法比向后甚至有限的差异方法（如果有人使用它们来解决这些问题）更有效，同时提供了更好的准确性和稳定性。
In this paper we derive semi-closed form prices of barrier (perhaps, time-dependent) options for the Hull-White model, ie., where the underlying follows a time-dependent OU process with a mean-reverting drift. Our approach is similar to that in (Carr and Itkin, 2020) where the method of generalized integral transform is applied to pricing barrier options in the time-dependent OU model, but extends it to an infinite domain (which is an unsolved problem yet). Alternatively, we use the method of heat potentials for solving the same problems. By semi-closed solution we mean that first, we need to solve numerically a linear Volterra equation of the first kind, and then the option price is represented as a one-dimensional integral. Our analysis shows that computationally our method is more efficient than the backward and even forward finite difference methods (if one uses them to solve those problems), while providing better accuracy and stability.
