Degree second order coherence is determined by the following expression
$$g^{(2)}(z) =\frac{\left<z\right|{a}^{+}{a}^{+}{a}{a}\left|z\right>} {\left<z\right|{a}^{+}{a}\left|z\right>^2}. $$
I want to calculate it for the case when $\left|z\right>$ is a squeezed state, i.e. $$\left|z\right> = {S}\left(z\right)\left|0\right>,$$ where $${S}\left(z\right) =e^{\frac{1}{2}z^{*}{a}^2 - \frac{1}{2}z{a}^{+2}}$$ is the squeeze operator, $\left|0\right>$ - the vacuum state, $z \in \mathbb{C}$.
I expect that $g^{(2)}(z) < 1$ but want to have the exact answer. Could anybody help me?