This paper shows that a small-time Hermite expansion is feasible for multivariate diffusions. By introducing an innovative quasi-Lamperti transform, which unitizes the diffusion matrix at the initial time, we derive explicit recursive formulas for the expansion coefficients of transition densities and European option prices for multivariate diffusions with jumps in return. These immediately available explicit formulas, particularly for the irreducbile, nonaffine, time-inhomogeneous model with different types of jump-size distribution, is new to the literature. The explicit formulas can lead to real-time derivatives pricing and hedging as well as model calibration. Extensive numerical experiments illustrate the accuracy and effectiveness of our approach.

本文表明，进行少量Hermite展开对于多元扩散是可行的。通过引入一种创新的准Lamperti变换，该变换在初始时间就将扩散矩阵统一了起来，我们得出了转换密度的扩展系数的显式递归公式，以及带有收益跳跃的多元扩散的欧洲期权价格。这些立即可用的显式公式，特别是对于具有不同类型的跳跃大小分布的不可归约，非仿射，时间不均匀模型而言，对于文献来说是新的。明确的公式可能会导致实时衍生产品定价和对冲以及模型校准。大量的数值实验说明了我们方法的准确性和有效性。