Equilibrium Asset Prices in a Continuous Time Portfolio Optimization Model with Decentralized Dealership Markets

The paper introduces a model of price formation in an economy with a decentralized dealership market for each of the traded securities, in continuous time. Each dealer is a competitive liquidity provider for non-dealer investors in the partial market for the given security. Quotes are in the form of strictly monotone pricing schedules. Both dealer and non-dealer investors have costly access to best quotes in the inter-dealer market. The dealers in a particular security have an advantage over other investors in that security in that they observe their respective private order flows of incoming trades. A dealer in a given security uses the observed order flow (coming jointly from other dealers and non-dealers) to improve the subjective estimates of relevant aggregate variables: the return on the security and the aggregate public (i.e. non-dealer) order flow. These sources of uncertainty have diffusion form and are dealt with according to principles of portfolio optimization in continuous time. Dealers are competitive, i.e. all agents are free to approach any dealer. I show how the dealership-based market structure leads to a modification of the traditional Consumption-based CAPM. In the case of informational customer-dealer asymmetries, I derive a formula for the deviation of the transaction price differential from the one prevailing in the full information case. The deviation is shown to be present even if the asymmetry only exists in the knowledge of the aggregate public order flow and does not concern the fundamentals.