HFT-52 · Week 42 · Market making

Skewing quotes by inventory

A market maker quotes around fair value and leans both quotes against its position. Skew pulls inventory back towards flat without giving up width; informed takers still pick it off, and the PnL split shows where the money went.

One market maker, seeded taker flow, 120 s session

Quotes vs fair value fair (mid)center = fair − skew·qbidasknoise fillinformed fill

Inventory (lots), whole session with your skewsame flow, no skewhard limit

PnL split, with your skew ($, 1 tick × 1 lot = $1) spread captureinventory (q × Δfair)total

Strategy	Max \|q\|	At limit	Spread	Inventory	Total	Fills	Informed

Prices are integer ticks ($0.01); fair value is the mid, a seeded random walk on the tick grid (100 ms steps). Quotes follow the drill: center = fair − skew · q, bid rounded down and ask rounded up from center ∓ half-spread, clamped post-only against a market of fair ± 1 tick, and the side that would add to |q| is pulled at the hard limit. Each quote is 1 lot. A noise taker hits a quote δ ticks from fair with probability 0.3·e^−0.6δ per step (the Avellaneda–Stoikov fill model). With informed flow the mid trends (up, down, up) and an informed taker arrives on 35% of steps, knows the mid 3 s ahead, and trades only when your quote is already wrong. PnL is attributed against the mid at fill time, so spread + inventory = total exactly; fees, queue position and latency are not modelled.