Before revision: The aim of this paper is to build dependent stochastic processes using the notion of self-decomposability in order to model dependence across different markets and extend some recently proposed multivariate L\'evy models based on subordination . Consequently, we study the properties of such processes, derive closed form expressions for  characteristic function and linear correlation coefficient and develop Monte Carlo schemes for their simulation. These results are instrumental to calibrate the models on power and gas energy European markets and to price spread options written on different underlying assets using Monte Carlo and Fourier techniques.
After revision: The aim of this paper is to build dependent stochastic processes using the notion of self-decomposability in order to model dependence across different markets and extend some recently proposed multivariate L\'evy models based on subordination . Consequently, we study the properties of such processes, derive closed form expressions for 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 Monte Carlo and Fourier techniques.