The increased trading in multi-name financial products has paved the way for the use of multivariate models that are at once computationally tractable and flexible enough to mimic the stylized facts of asset log-returns and of their dependence structure. In this paper we propose a new multivariate Lévy model, the so-called \(\varDelta \)-Gamma model, where the log-price gains and losses are modeled by separate multivariate Gamma processes, each containing a common and an idiosyncratic component. Furthermore, we extend this multivariate model to the Sato setting, allowing for a moment term structure that is more in line with empirical evidence. We calibrate the two models on single-name option price surfaces and market implied correlations and we show how the \(\varDelta \)-Gamma Sato model outperforms its Lévy counterpart, especially during periods of market turmoil. The numerical study also reveals the advantages of these new types of multivariate models, compared to a multivariate VG model.

中文翻译：

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朝向$$ \ Delta $$Δ-Gamma Sato多元模型

多名称金融产品交易的增加为使用多元模型铺平了道路，该模型可立即在计算上易于处理且具有足够的灵活性以模仿资产对数返还及其依赖结构的典型事实。在本文中，我们提出了一种新的多元Lévy模型，即所谓的\（\ varDelta \）- Gamma模型，其中对数价格损益由单独的多元Gamma过程建模，每个过程都包含一个共同的和一个特有的成分。此外，我们将此多元模型扩展到Sato设置，从而使矩项结构更符合经验证据。我们在单一名称期权价格表面和市场隐含相关性上校准了两个模型，并展示了\（\ varDelta \）-Gamma Sato模型优于其Lévy模型，尤其是在市场动荡时期。数值研究还揭示了与多变量VG模型相比，这些新型的多变量模型的优势。