Quoting when one fill in three runs you over

Question

You're quoting in a jumpy market. You estimate that $30\%$ of the time your next fill is a "run", the value gaps $\$ 0.20 $against your new position before you can react. The other **$ 70%$ of the time** the fill is benign and you simply keep your half-spread.

At a $5$ -cent half-spread, what's your EV per fill? What half-spread do you need to break even?

Accepted Answer

EV at a 5-cent half-spread. On a benign fill (70\%) you keep the half-spread s = 0.05. On a run (30\%) you still collect the half-spread but then eat the \0.20 gap, netting s - 0.20 = 0.05 - 0.20 = -0.15: E[	ext{profit}] = 0.70(0.05) + 0.30(0.05 - 0.20) = 0.035 + 0.30(-0.15) = 0.035 - 0.045 = -\0.01. You lose a penny per fill. A 5-cent half-spread isn't enough when nearly a third of fills gap a dime against you. Break-even half-spread. Collect s on every fill; lose the gap G = 0.20 on the 30\% that run: E[	ext{profit}] = s - 0.30\,G = s - 0.30(0.20) = s - 0.06. Setting this to zero: s^ = 0.…

Quoting when one fill in three runs you over

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