Based on the concept of self-decomposability, we extend some recent multivariate Lévy models built using multivariate subordination with the aim of capturing situations in which a sudden event in one market is propagated onto related markets after a certain stochastic time delay. Consequently, we study the properties of such processes, derive closed form expressions for the characteristic function and detail how a Monte Carlo scheme can be easily implemented. We illustrate the applicability of our approach in the context of gas and power Energy markets focusing on the calibration and on the pricing of spread options written on different underlying assets using simulations techniques.