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How far should a long book drag your quotes?

Asked at Optiver

You make markets in a stock worth 50.0050.00. Flat, you'd quote 49.9649.96 / 50.0450.04. Random flow has left you long 4,0004{,}000 shares, more than you'd like, and you still believe fair value is exactly 50.0050.00.

Model your reservation price (the price you're truly indifferent to trading at) as fair value shifted by kqk \cdot q, where qq is your signed inventory and k = \0.00001$ per share is a risk coefficient.

Where do you center your quotes now, and what does the shift depend on?

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