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Weighted mid after the next event
The best bid is with a size of units and the best ask is with a size of units. The next event is, with probability each, a market order that removes units from the ask, or a market order that removes units from the bid. The weighted mid price is the bid times the ask size, plus the ask times the bid size, all divided by the sum of the sizes. What is the expected weighted mid price after the event? Give a decimal.
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Hint
Compute the weighted mid price in each branch, then average the branches.
Solution
- If the ask loses , sizes are on the bid and on the ask, giving .
- If the bid loses , sizes are on the bid and on the ask, giving .
- The average is .
Answer: