Asymptotic stability of the zero solution for stochastic jump parameter systems of differential equations given by dX(t) = A(ξ(t))X(t) dt + H(ξ(t))X(t) dw(t), where ξ(t) is a finite-valued Markov process and w(t) is a standard Wiener process, is considered. It is proved that the existence of a unique positive solution of the system of coupled Lyapunov matrix equations derived in the paper is a necessary asymptotic stability condition.