You just got lifted, why should you move your quotes?

Question

You're making a market in an interview game on some unknown quantity. You quote $48$ bid, at $52$ . The interviewer lifts your offer (buys at $52$ ), 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 up, e.g. to 50 at 54. Two separate forces point the same way: 1. Information (Bayesian updating). The counterparty chose to buy at 52 rather than sell at 48 or pass. If there's any chance they know something, "they bought" is evidence the true value exceeds 52. Your posterior fair value must rise: E[V \mid 	ext{they bought at } 52] E[V]. Re-quoting 48 at 52 ignores information you just paid to receive. If they lift you again at 54, update again, the sequence of one-sided trades is a random walk of evidence that your fair is too low. 2. Inventory (risk management). You …

You just got lifted, why should you move your quotes?

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