We model the execution of a large uninformed sell order in the presence of strategic competitive market makers. We solve for the unique symmetric equilibrium of the model in closed form. Analysis of this equilibrium reveals that large orders unequivocally benefit market makers, while smaller investors stand to benefit only if the order trades with a sufficiently high intensity. The equilibrium results further provide a rationale for the empirically observed patterns of (1) shorter orders trading at higher intensities and (2) price pressures potentially subsiding before large orders stop executing.
This paper studies the optimal investment problem with random endowment in an inventory‐based price impact model with competitive market makers. Our goal is to analyze how price impact affects optimal policies, as well as both pricing rules and demand schedules for contingent claims. For exponential market makers preferences, we establish two effects due to price impact: constrained trading and nonlinear hedging costs. To the former, wealth processes in the impact model are identified with those in a model without impact, but with constrained trading, where the (random) constraint set is generically neither closed nor convex. Regarding hedging, nonlinear hedging costs motivate the study of arbitrage free prices for the claim. We provide three such notions, which coincide in the frictionless case, but which dramatically differ in the presence of price impact. Additionally, we show arbitrage opportunities, should they arise from claim prices, can be exploited only for limited position sizes, and may be ignored if outweighed by hedging considerations. We also show that arbitrage‐inducing prices may arise endogenously in equilibrium, and that equilibrium positions are inversely proportional to the market makers' representative risk aversion. Therefore, large positions endogenously arise in the limit of either market maker risk neutrality, or a large number of market makers.
more » « less- PAR ID:
- 10454298
- Publisher / Repository:
- Wiley-Blackwell
- Date Published:
- Journal Name:
- Mathematical Finance
- Volume:
- 31
- Issue:
- 1
- ISSN:
- 0960-1627
- Page Range / eLocation ID:
- p. 3-35
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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