Peter Cotton from J.P. Morgan.
Paper: Trading Illiquid Goods: Market Making as a Sequence of Sealed-Bid Auctions, with Analytic Results
We provide analytic results for the optimal control problem faced by a market maker who can only obtain and dispose of inventory via a sequence of sealed-bid auctions. Under the assumption that the best competing response is exponentially distributed around a commonly discerned fair market price we examine properties of the market maker’s optimal behavior. We show that simple adjustments to skew and width accommodate customer arrival imbalance. We derive a straightforward relationship between the market marker’s fill probability and direct holding costs. A simple formula for optimal bidding in terms of inventory cost is presented. We present the results as a perturbation of an improvement to a “linear skew, constant width” (CWLS) market making heuristic.