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摘要翻译：
本文讨论拟蒙特卡罗方法在Heston模型中的应用。我们的算法基于Broadie-Kaya算法，这是一种精确的Heston模型仿真方案。由于联合转移密度不是封闭形式的，在价格过程服从Heston模型的情况下，由Imai和Tan提出的提高拟蒙特卡罗方法有效性的线性变换方法不能用于路径依赖期权。因此，我们将拟蒙特卡罗方法直接用于Heston模型。本文的主要贡献有三个方面：首先，我们展示了如何在Heston模型和SVJ模型的背景下应用拟蒙特卡罗方法；其次，拟蒙特卡罗方法对蒙特卡罗方法的改进；第三，如何利用适合Heston模型和SVJ模型的桥梁结构来提高拟蒙特卡罗方法的有效性。最后，我们给出了计算希腊语、障碍期权、多维多资产定价和3/2模型的一些扩展。
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英文标题：
《Quasi-Monte Carlo methods for the Heston model》
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作者：
Jan Baldeaux and Dale Roberts
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最新提交年份：
2012
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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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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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PDF链接：
https://arxiv.org/pdf/1202.3217
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