Papers and working notes of the program, most recent first.
A market maker trades only by responding to sealed-bid enquiries arriving with imbalanced intent. The imbalanced problem compresses exactly onto the balanced one: skew translates by δ = (w/2) log(q/(1−q)), quotes widen by γ, and the cost of carry multiplies by 1/(2√(q(1−q))). A flat book still skews; skew is first order in imbalance while width is second; the constant-width linear-skew benchmark is a corner case.
Extends the model to clustered arrivals and stochastically varying imbalance, and develops the analytic structure of the indifference cost ν(x) whose slope is the quoted skew and whose convexity is the discretionary width.
For goods whose physical carry is tens of basis points, what keeps optimal inventory bounded? The dealer market's bid–offer as the endogenous replacement for the missing carrying cost; the imbalance multiplier; the oscillator reading of the commodity cycle; hypotheses and a scoreboard.
The storage relation as a term-structure constraint, transport of the coverage-forecast curve, volatility and width constraints, an MFG aggregation conjecture, the explosiveness boundary, and the filtering problem when flows are observed but the stock is latent.
@unpublished{cotton2026skew,
author = {Cotton, Peter},
title = {On a Simple Relationship Between Order Imbalance,
Skew and Width in Over-The-Counter Trading},
note = {Working paper; work completed around 2015,
first written up 2022},
year = {2026},
url = {https://github.com/microprediction/inventory}
}