Uninformed flow, but you are badly short
Asked at Optiver, IMC
You are running a market-making game. Over the last few rounds your offer has been lifted five times in a row, and you are now short five units. Before your next quote the interviewer says: "Just so you know, I decide buy or sell by flipping a coin. There is no information in my trades."
Given that, should you still move your quotes off the fair value? Which way, and why?
Show a hint
Take the interviewer at their word: reason one (adverse selection) is switched off. Does anything still push you to skew?
Your answer
This one is open-ended. Work it through, then check your reasoning against the full solution.