英文标题：
《The Multivariate Mixture Dynamics Model: Shifted dynamics and
  correlation skew》
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作者：
Damiano Brigo, Camilla Pisani, Francesco Rapisarda
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最新提交年份：
2018
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英文摘要：
  The Multi Variate Mixture Dynamics model is a tractable, dynamical, arbitrage-free multivariate model characterized by transparency on the dependence structure, since closed form formulae for terminal correlations, average correlations and copula function are available. It also allows for complete decorrelation between assets and instantaneous variances. Each single asset is modelled according to a lognormal mixture dynamics model, and this univariate version is widely used in the industry due to its flexibility and accuracy. The same property holds for the multivariate process of all assets, whose density is a mixture of multivariate basic densities. This allows for consistency of single asset and index/portfolio smile. In this paper, we generalize the MVMD model by introducing shifted dynamics and we propose a definition of implied correlation under this model. We investigate whether the model is able to consistently reproduce the implied volatility of FX cross rates once the single components are calibrated to univariate shifted lognormal mixture dynamics models. We consider in particular the case of the Chinese renminbi FX rate, showing that the shifted MVMD model correctly recovers the CNY/EUR smile given the EUR/USD smile and the USD/CNY smile, thus highlighting that the model can also work as an arbitrage free volatility smile extrapolation tool for cross currencies that may not be liquid or fully observable. We compare the performance of the shifted MVMD model in terms of implied correlation with those of the shifted Simply Correlated Mixture Dynamics model where the dynamics of the single assets are connected naively by introducing correlation among their Brownian motions. Finally, we introduce a model with uncertain volatilities and correlation. The Markovian projection of this model is a generalization of the shifted MVMD model.
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中文摘要：
多变量混合动力学模型是一个易于处理的、动态的、无套利的多变量模型，其特点是依赖结构的透明性，因为终端相关性、平均相关性和copula函数的封闭式公式是可用的。它还允许资产和瞬时方差之间完全不相关。每个单一资产都是根据对数正态混合动力学模型建模的，这种单变量模型因其灵活性和准确性在行业中得到广泛应用。所有资产的多元过程也具有相同的性质，其密度是多元基本密度的混合物。这使得单一资产和指数/投资组合保持一致。在本文中，我们通过引入移位动力学来推广MVMD模型，并在此模型下提出了隐含相关性的定义。我们研究了当单一成分被校准为单变量移位对数正态混合动力学模型后，该模型是否能够一致地再现外汇交叉汇率的隐含波动性。我们特别考虑了中国人民币汇率的情况，表明考虑到欧元/美元和美元/人民币的微笑，转移后的MVMD模型正确地恢复了人民币/欧元的微笑，从而强调该模型也可以作为无套利波动率微笑外推工具，用于可能不具有流动性或完全可观察的跨货币。我们比较了移位MVMD模型在隐含相关性方面的性能，以及移位简单相关混合动力学模型的性能，后者通过引入布朗运动之间的相关性，将单个资产的动力学简单地连接起来。最后，我们介绍了一个波动率和相关性不确定的模型。该模型的马尔可夫投影是移位MVMD模型的推广。
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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：Risk Management        风险管理
分类描述：Measurement and management of financial risks in trading, banking, insurance, corporate and other applications
衡量和管理贸易、银行、保险、企业和其他应用中的金融风险
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