Dealing with the Inventory Risk. A solution to the market making problem

Olivier Gu\'eant, Charles-Albert Lehalle and Joaquin Fernandez Tapia

Papers from arXiv.org

Abstract: Market makers continuously set bid and ask quotes for the stocks they have under consideration. Hence they face a complex optimization problem in which their return, based on the bid-ask spread they quote and the frequency at which they indeed provide liquidity, is challenged by the price risk they bear due to their inventory. In this paper, we consider a stochastic control problem similar to the one introduced by Ho and Stoll and formalized mathematically by Avellaneda and Stoikov. The market is modeled using a reference price $S_t$ following a Brownian motion with standard deviation $\sigma$, arrival rates of buy or sell liquidity-consuming orders depend on the distance to the reference price $S_t$ and a market maker maximizes the expected utility of its P&L over a finite time horizon. We show that the Hamilton-Jacobi-Bellman equations associated to the stochastic optimal control problem can be transformed into a system of linear ordinary differential equations and we solve the market making problem under inventory constraints. We also shed light on the asymptotic behavior of the optimal quotes and propose closed-form approximations based on a spectral characterization of the optimal quotes.

Date: 2011-05, Revised 2012-08
New Economics Papers: this item is included in nep-bec and nep-mst
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (29)

Downloads: (external link)
http://arxiv.org/pdf/1105.3115 Latest version (application/pdf)

Related works:
Working Paper: Dealing with the Inventory Risk. A solution to the market making problem (2013)
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:1105.3115

Access Statistics for this paper

More papers in Papers from arXiv.org
Bibliographic data for series maintained by arXiv administrators ().