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Bid size for a target

Market makingMedium

The best bid is $100$ and the best ask is $101$ , with $20$ units resting at the ask. A pricing rule places the fair price at the bid plus the spread times the share of total resting size that sits at the bid. What bid size, in units, puts that fair price at exactly $100.6$ ?

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Hint

The bid share must equal the distance above the bid divided by the spread.

Solution

The spread is $101 - 100 = 1$ , so the bid share of the total size must be $0.6$ .
With bid size s, this gives $s \div (s + 20) = 0.6$ , so $0.4 s = 12$ .
The bid size is $30$ .

Answer: $30$

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