This paper introduces a class of multivariate GARCH models that extends the existing literature by explicitly modeling correlation dependent pricing kernels. A large subclass admits closed-form recursive solutions for the moment generating function under the risk-neutral measure, which permits efficient pricing of multi-asset options. We perform a full calibration to three bivariate series of index returns and their corresponding volatility indexes in a joint maximum likelihood estimation. The results empirically confirm the presence of correlation dependance in addition to the well known variance dependance in the pricing kernel. The model improves both the overall likelihood and the VIX-implied likelihoods, with a better fitting of marginal distributions, e.g., 15% less error on one-asset option prices. The new degree of freedom is also shown to significantly impact the shape of marginal and joint pricing kernels, and leads to up to 53% differences for out-of-the-money two-asset correlation option prices.

本文介绍了一类多元 GARCH 模型，该模型通过显式建模相关依赖定价核来扩展现有文献。一个大的子类允许在风险中性措施下的时刻生成函数的封闭形式递归解决方案，这允许多资产期权的有效定价。我们在联合最大似然估计中对三个双变量系列指数回报及其相应的波动率指数进行了全面校准。结果从经验上证实，除了定价内核中众所周知的方差依赖性之外，还存在相关性依赖性。该模型提高了整体可能性和 VIX 隐含可能性，更好地拟合边际分布，例如，单一资产期权价格的误差减少了 15%。