Heston模型的拟蒙特卡罗方法
Quasi-Monte Carlo methods for the Heston model
摘要：
本文讨论了拟蒙特卡罗方法在Heston模型中的应用。我们的基础上Broadie-Kaya算法，赫斯顿模型的精确模拟计划，我们的算法。由于联合转移密度不能以封闭形式获得，Imai和Tan的线性变换方法，一种流行且广泛适用的方法，用于提高拟蒙特卡罗方法的有效性，不能在基础价格过程遵循Heston模型的路径依赖期权的背景下使用。因此，我们定制拟蒙特卡罗方法直接到赫斯顿模型。本文的贡献有三个方面：首先，我们展示了如何应用拟蒙特卡罗方法的赫斯顿模型和SVJ模型的背景下，第二，拟蒙特卡罗方法改进蒙特卡罗方法，第三，如何提高拟蒙特卡罗方法的有效性，通过使用适合赫斯顿和SVJ模型的桥梁结构。最后，我们提供了计算希腊，障碍期权，多维和多资产定价，和3/2模型的一些扩展。
英文摘要：
In this paper, we discuss the application of quasi-Monte Carlo methods to the Heston model. We base our algorithms on the Broadie-Kaya algorithm, an exact simulation scheme for the Heston model. As the joint transition densities are not available in closed-form, the Linear Transformation method due to Imai and Tan, a popular and widely applicable method to improve the effectiveness of quasi-Monte Carlo methods, cannot be employed in the context of path-dependent options when the underlying price process follows the Heston model. Consequently, we tailor quasi-Monte Carlo methods directly to the Heston model. The contributions of the paper are threefold: We firstly show how to apply quasi-Monte Carlo methods in the context of the Heston model and the SVJ model, secondly that quasi-Monte Carlo methods improve on Monte Carlo methods, and thirdly how to improve the effectiveness of quasi-Monte Carlo methods by using bridge constructions tailored to the Heston and SVJ models. Finally, we provide some extensions for computing greeks, barrier options, multidimensional and multi-asset pricing, and the 3/2 model.
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