Papers

The core write-ups of the program. For the wider literature — antecedents, the optimal market making line, and the probability side — see the bibliography.

Core

Cotton, P. (2026). On a Simple Relationship Between Order Imbalance, Skew and Width in Over-The-Counter Trading. Working paper; work completed around 2015, first written up 2022. tex · numerical certificate · demos: symmetry, simulation. The imbalance equivalence: with sellers arriving at probability $q$, the steady-state market making problem compresses exactly onto the balanced one under a skew translation $\delta = \tfrac{w}{2}\log\tfrac{q}{1-q}$, a quote widening $\gamma$, and a carrying-cost multiplier $1/(2\sqrt{q(1-q)})$. A flat book still skews; skew is first order in imbalance while width is second; constant-width linear-skew is a corner case.
Cotton, P. (2026). Exponential Rigidity and a Log-Value Normal Form for Imbalanced Market Making. Working paper. tex · numerical certificate. The coordinate $\Phi=-\log(G/G_\star)$ turns buy–sell imbalance into an exact translation of two log-value coordinates. The translation is induced by state-independent strike shifts exactly for exponential-plus-constant enquiry value, and rationalizability forces the constant to zero; a perturbation hierarchy on the inventory lattice runs on a single linear operator, and reflection symmetry makes skew odd and the width response even in the log-odds of the flow.
Cotton, P., and Papanicolaou, A. Trading Illiquid Goods: Market Making as a Sequence of Sealed-Bid Auctions, with Analytic Results. Working paper, under revision as the extension of Cotton (2026a) — deck. Extends the model to clustered arrivals and stochastically varying imbalance, and develops the indifference cost $\nu(x)$ whose slope is the quoted skew and whose convexity is the discretionary width.