摘要翻译:
本文致力于用蒙特卡罗和马利亚文演算对美式期权进行定价。与大多数与此主题相关的文章不同,在本文中,我们不会使用本地化字体来减少差异。我们的方法是基于条件期望E[F(St)/SS]的非局部化Malliavin演算。然后利用封闭公式、基于条件的技术和对模拟路径数的明智选择来减小E[F(St)/SS]估计量的方差。最后,我们执行停止时间版本的动态规划算法,以减少偏差。一方面,我们将发展具有确定性且无常系数的指数多维扩散的Malliavin演算工具。另一方面,我们将详细介绍各种非参数技术来减少方差。此外,我们将在一个异构CPU/GPU多核机上测试我们方法的数值效率。
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英文标题:
《American Options Based on Malliavin Calculus and Nonparametric Variance
Reduction Methods》
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作者:
Lokman Abbas-Turki (LAMA), Bernard Lapeyre (CERMICS)
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最新提交年份:
2011
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分类信息:
一级分类:Quantitative Finance 数量金融学
二级分类:Pricing of Securities 证券定价
分类描述:Valuation and hedging of financial securities, their derivatives, and structured products
金融证券及其衍生产品和结构化产品的估值和套期保值
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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 is devoted to pricing American options using Monte Carlo and the Malliavin calculus. Unlike the majority of articles related to this topic, in this work we will not use localization fonctions to reduce the variance. Our method is based on expressing the conditional expectation E[f(St)/Ss] using the Malliavin calculus without localization. Then the variance of the estimator of E[f(St)/Ss] is reduced using closed formulas, techniques based on a conditioning and a judicious choice of the number of simulated paths. Finally, we perform the stopping times version of the dynamic programming algorithm to decrease the bias. On the one hand, we will develop the Malliavin calculus tools for exponential multi-dimensional diffusions that have deterministic and no constant coefficients. On the other hand, we will detail various nonparametric technics to reduce the variance. Moreover, we will test the numerical efficiency of our method on a heterogeneous CPU/GPU multi-core machine.
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PDF链接:
https://arxiv.org/pdf/1104.5131