灵敏度的双核估计

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摘要翻译：
本文讨论了估计随机变量的期望相对于描述其演化的参数的敏感性的一般问题。例如，在金融学中，未定权益价格的敏感性被称为希腊人。最近，Elie，Fermanian和Touzi通过将感兴趣的参数随机化并结合非参数估计技术引入了一种新的估计希腊人的方法。本文研究了另一类与得分函数密切相关的估计量，即最优希腊权重。该估计依赖于使用两个不同的核函数，本文的主要兴趣是给出它的渐近性质。在更严格的条件下，其收敛速度与Elie、Fermanian和Touzi所提出的收敛速度相当，并优于有限差分估计。除了证明的技术兴趣之外，这一结果在为灵敏度创建新类型估计量的动态中也是非常令人鼓舞的。
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英文标题：
《Double Kernel estimation of sensitivities》
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作者：
Romuald Elie (CREST, Ceremade)
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最新提交年份：
2009
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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 adresses the general issue of estimating the sensitivity of the expectation of a random variable with respect to a parameter characterizing its evolution. In finance for example, the sensitivities of the price of a contingent claim are called the Greeks. A new way of estimating the Greeks has been recently introduced by Elie, Fermanian and Touzi through a randomization of the parameter of interest combined with non parametric estimation techniques. This paper studies another type of those estimators whose interest is to be closely related to the score function, which is well known to be the optimal Greek weight. This estimator relies on the use of two distinct kernel functions and the main interest of this paper is to provide its asymptotic properties. Under a little more stringent condition, its rate of convergence equals the one of those introduced by Elie, Fermanian and Touzi and outperforms the finite differences estimator. In addition to the technical interest of the proofs, this result is very encouraging in the dynamic of creating new type of estimators for sensitivities.
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PDF链接：
https://arxiv.org/pdf/0909.2624

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关键词：核估计 灵敏度 Applications Quantitative Differential estimator 本文 技术 兴趣 得分