Call bounds in a three-outcome one-step model

Rates are zero and a stock at $100$ can move in one step to $90$, $100$ or $110$. What can you say about the no-arbitrage price of a call struck at $100$?

Only that it lies strictly between $0$ and $5$. The market is incomplete: risk-neutral probabilities must satisfy $110q_u+100q_m+90q_d=100$, which forces $q_u=q_d$, with $q_u\in(0,\tfrac12)$. The call pays $10$ only in the up state, so its price $10q_u$ can be anything in $(0,5)$ without arbitrage.