Optimal bid-ask placement

MediumMarket Making & Betting Games~5m

You believe fair value is $100 and you quote a spread $s$ symmetrically around it. Your edge per uninformed fill is $s/2$ , but a wider spread gets fewer fills. What trade-off sets the optimal spread?

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Wider spread: more edge each fill, but fewer fills.
Optimize total expected profit = edge × volume.

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Balance edge per fill against fill probability (volume)

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Optimal bid-ask placement

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