Assuming that the asset price $X$ follows a constant elasticity of variance process, this paper studies the optimal prediction problem $\inf_{0\leq τ\leq T}\mathbb{E}|X_τ-\ell|$, where the infimum is taken over stopping times $τ$ of $X$ and $\ell$ is a hidden aspiration level independent of $X$. Adopting the aspiration level hypothesis, we show that a class of admissible laws of $\ell$ leads to optimal trading boundaries which are located relative to the median interval of $\ell$ and serve as predictors of the resistance and support levels. The existence of these boundaries is proved and nonlinear integral equations are derived to characterise them uniquely. In the positive drift case the stopping set is bounded by two curves, while in the negative drift case the stopping set is described by a single boundary.
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