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摘要翻译：
本文研究了多个分层方向作为方差减少技术的使用，用于高斯向量驱动的路径相关期权的蒙特卡罗模拟。该方法的精度取决于分层方向和各层内分配规则的选择。已经提出了几种选择，但是，即使它们提供了方差减少，它们的实现是计算密集型的，不适用于现实的收益，尤其不适用于有障碍的亚式期权。此外，所有这些以前发表的方法都采用正交方向进行多层化。在这项工作中，我们研究了产生方便的方向的算法的使用，通常是非正交的，结合了较低的计算代价和可比的方差减少。此外，我们还研究了与拉丁超立方抽样相比，在方差减少方面最优分配的准确性。我们考虑了通过线性变换和主成分分析得到的方向。我们提出了一个新的程序，基于线性逼近的解释方差的总方差定律。此外，我们展示了一个新的算法，允许正确地生成沿非正交方向分层的法向量。最后，在Black-Scholes和Cox-Ingersoll-Ross市场中，我们证明了这些算法在计算有障碍和无障碍的不同路径依赖期权价格时的有效性。
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英文标题：
《Convenient Multiple Directions of Stratification》
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作者：
Benjamin Jourdain, Bernard Lapeyre and Piergiacomo Sabino
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最新提交年份：
2010
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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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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
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英文摘要：
This paper investigates the use of multiple directions of stratification as a variance reduction technique for Monte Carlo simulations of path-dependent options driven by Gaussian vectors. The precision of the method depends on the choice of the directions of stratification and the allocation rule within each strata. Several choices have been proposed but, even if they provide variance reduction, their implementation is computationally intensive and not applicable to realistic payoffs, in particular not to Asian options with barrier. Moreover, all these previously published methods employ orthogonal directions for multiple stratification. In this work we investigate the use of algorithms producing convenient directions, generally non-orthogonal, combining a lower computational cost with a comparable variance reduction. In addition, we study the accuracy of optimal allocation in terms of variance reduction compared to the Latin Hypercube Sampling. We consider the directions obtained by the Linear Transformation and the Principal Component Analysis. We introduce a new procedure based on the Linear Approximation of the explained variance of the payoff using the law of total variance. In addition, we exhibit a novel algorithm that permits to correctly generate normal vectors stratified along non-orthogonal directions. Finally, we illustrate the efficiency of these algorithms in the computation of the price of different path-dependent options with and without barriers in the Black-Scholes and in the Cox-Ingersoll-Ross markets.
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PDF链接：
https://arxiv.org/pdf/1004.5037
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