A general method is presented to compute the variance of a linear stochastic process through a matrix Lyapunov differential equation. This approach, adopted from control theory, is alternative and easier with respect to the classical arguments found in quantitative finance literature and can be readily applied to high-dimensional models. Both analytical and numerical methods to solve the Lyapunov equation are discussed and compared in terms of computational efficiency. A practical application is presented, where numerical and analytical solutions for the variance of a two-factor mean-reverting model are embedded into the Black pricing framework and market calibration of model parameters is performed. It is shown that the availability of an analytical formula for the variance makes the calibration 14 times faster, thus proving the practical value of tractable and general methods to derive it.
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