When the tick won't let you quote your fair price

Question

Your model says the ideal offer, the price that best balances edge against fill probability, is $50.023$ . But the tick is $\$ 0.01 $, so you can only post$ 50.02 $or$ 50.03 $. Fair value (the mid) is$ 50.00$.

At $50.02$ you estimate a $60\%$ fill probability; at $50.03$ , a $45\%$ fill probability.

Which should you post, and what does the tick constraint cost you?

Accepted Answer

Score each legal price by EV = (fill probability) × (edge over fair). Post 50.02 (edge = 50.02 - 50.00 = 2 cents, fill prob 60\%): 0.60 	imes 0.02 = 0.012 = 1.20 	ext{ cents of expected edge per share.} Post 50.03 (edge = 3 cents, fill prob 45\%): 0.45 	imes 0.03 = 0.0135 = 1.35 	ext{ cents of expected edge per share.} Post 50.03, it wins, 1.35 vs 1.20 cents. Even though rounding up from 50.023 to 50.03 costs some fill probability, the extra cent of edge on the fills you do get more than compensates here. (The answer isn't automatic: if the fill probabilities were 70\% at 50.02 vs 40\% at…

When the tick won't let you quote your fair price

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