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摘要翻译：
高斯Copula在工业中被广泛地应用于当两个随机变量之间的相关性不存在先验知识时，将它们关联起来。扰动高斯copula方法允许将两个随机变量的偏斜信息引入到相关结构中。在一个共同的快速均值恢复随机波动因子的假设下，通过渐近展开导出了该copula的解析表达式。本文将这种新的扰动copula应用于衍生产品的估值；尤其是第三种货币的FX quanto期权。给出了一个校正过程来拟合两个基础证券的倾斜。通过与高斯copula的比较，解释了扰动copula的作用。通过一个实际算例，比较了copulas和一个具有恒定相关性的局部波动率模型在不同期限、相关性和倾斜配置下的波动率。
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英文标题：
《Perturbed Copula: Introducing the skew effect in the co-dependence》
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作者：
Alberto Elices, Jean-Pierre Fouque
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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：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：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：
Gaussian copulas are widely used in the industry to correlate two random variables when there is no prior knowledge about the co-dependence between them. The perturbed Gaussian copula approach allows introducing the skew information of both random variables into the co-dependence structure. The analytical expression of this copula is derived through an asymptotic expansion under the assumption of a common fast mean reverting stochastic volatility factor. This paper applies this new perturbed copula to the valuation of derivative products; in particular FX quanto options to a third currency. A calibration procedure to fit the skew of both underlying securities is presented. The action of the perturbed copula is interpreted compared to the Gaussian copula. A real worked example is carried out comparing both copulas and a local volatility model with constant correlation for varying maturities, correlations and skew configurations.
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PDF链接：
https://arxiv.org/pdf/1003.0041
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