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.

多名称金融产品交易的增加为多元模型的使用铺平了道路，这些模型在计算上易于处理且足够灵活，足以模仿资产对数回报及其依赖结构的程式化事实。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，其中对数价格收益和损失是通过单独的多元 Gamma 过程建模的，每个过程都包含一个共同的和一个特殊的组件。此外，我们将这个多元模型扩展到佐藤设置，允许更符合经验证据的矩期限结构。我们在单一名称期权价格表面和市场隐含相关性上校准这两个模型，并展示了\(\varDelta \) -Gamma Sato 模型如何优于其 Lévy 模型，尤其是在市场动荡时期。数值研究还揭示了与多元 VG 模型相比，这些新型多元模型的优势。