Before revision: A general method is presented to compute the variance of a linear stochastic process through a matrix Lyapunov differential equation.
After revision: Energy companies need efficient procedures to perform market calibration of stochastic models for commodities. If the Black framework is chosen for option pricing, the bottleneck of market calibration is the computation of the variance of the asset. For energy commodities, it is common to adopt multi-factor linear models, whose variance obeys a matrix Lyapunov differential equation.