摘要翻译：
我们研究了Malliavin演算的应用，以便通过模拟计算多维复杂路径相关期权的希腊语。为此，我们将Montero和Kohatsu-Higa的公式推广到多维情形。多维设置显示了Malliavin演算方法相对于以前提出的不同技术的便利性。实际上，这些技术可能在计算上是昂贵的，并且不提供方差减少的灵活性。相比之下，Malliavin方法通过提供一类函数以不同的精确度返回相同的期望值（希腊语）而表现出更高的灵活性。如果不使用Malliavin微积分的广义部分积分公式，这种方差约简的通用性是不可能的。在多维背景下，我们找到了方便的公式，可以改进Fourni\'e等人提出的定位技术，并减少计算开销和方差。此外，我们还证明了用于方差减少的参数可以在仿真中得到。在多维Black-Scholes市场中，我们证明了所提出的方法的有效性，并结合Sabino中所讨论的准蒙特卡罗模拟的增强版本，对具有固定和浮动执行价格的看涨期权、数字亚洲式和异国情调篮子期权的增量进行了数值估计。
---
英文标题：
《Multidimensional Quasi-Monte Carlo Malliavin Greeks》
---
作者：
Nicola Cufaro Petroni and Piergiacomo Sabino
---
最新提交年份：
2011
---
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
--
一级分类：Mathematics        数学
二级分类：Probability        概率
分类描述：Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory
概率论与随机过程的理论与应用：例如中心极限定理，大偏差，随机微分方程，统计力学模型，排队论
--

---
英文摘要：
  We investigate the use of Malliavin calculus in order to calculate the Greeks of multidimensional complex path-dependent options by simulation. For this purpose, we extend the formulas employed by Montero and Kohatsu-Higa to the multidimensional case. The multidimensional setting shows the convenience of the Malliavin Calculus approach over different techniques that have been previously proposed. Indeed, these techniques may be computationally expensive and do not provide flexibility for variance reduction. In contrast, the Malliavin approach exhibits a higher flexibility by providing a class of functions that return the same expected value (the Greek) with different accuracies. This versatility for variance reduction is not possible without the use of the generalized integral by part formula of Malliavin Calculus. In the multidimensional context, we find convenient formulas that permit to improve the localization technique, introduced in Fourni\'e et al and reduce both the computational cost and the variance. Moreover, we show that the parameters employed for variance reduction can be obtained \textit{on the flight} in the simulation. We illustrate the efficiency of the proposed procedures, coupled with the enhanced version of Quasi-Monte Carlo simulations as discussed in Sabino, for the numerical estimation of the Deltas of call, digital Asian-style and Exotic basket options with a fixed and a floating strike price in a multidimensional Black-Scholes market.
---
PDF链接：
https://arxiv.org/pdf/1103.5722