A definable henselian valuation with high quantifier complexity

We give an example of a parameter-free definable henselian valuation ring which is neither definable by a parameter-free $\mathrm{\forall }\mathrm{\exists }$-formula nor by a parameter-free $\mathrm{\exists }\mathrm{\forall }$-formula in the language of rings. This answers a question of Prestel.