Your bid just got hit, which way do you re-quote?

Question

You are making a market in an interview game on some unknown quantity. You quote $48$ bid, at $52$ . The interviewer hits your bid (sells to you at $48$ ), then asks: "Make me a new market."

Should your new quotes differ from 48 at 52? Why? Give two independent reasons.

Accepted Answer

Yes, shade both quotes down, for example to 46 at 50. Two separate forces agree: 1. Information (Bayesian updating). The counterparty chose to sell at 48 rather than buy at 52 or pass. If they might know something, "they sold" is evidence the true value is below 48. Your posterior fair value must fall: E[V \mid 	ext{they sold at } 48] < E[V]. Leaving your quotes at 48 at 52 throws away information you just paid to receive. If they hit your bid again at 46, update again; a run of one-sided sells is a walk of evidence that your fair is too high. 2. Inventory (risk management). You are now long…

Your bid just got hit, which way do you re-quote?

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