Dealing with the inventory risk: a solution to the market making problem
By Olivier Guéant, Charles-Albert Lehalle, J. Fernandez-Tapia. 2011
236 citations recorded by the source corpus.
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 (J Fin Econ 9(1): 47–73, 1981) and formalized mathematically by Avellaneda and Stoikov (Quant Fin 8(3):217–224, 2008). The market is modeled using a reference price St following a Brownian motion with standard deviation σ, arrival rates of buy or sell liquidity-consuming orders depend on the distance to the reference price St 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.
Subfields: Finance
View Paper: https://www.semanticscholar.org/paper/507afa808cb52cd6ba690ed07e7d83a3fb6bec81
How researchers see this paper
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In Finance
- Ben M. Hambly
- Ryan Donnelly
- Á. Cartea
- Huining Yang
- Sebastian Jaimungal
- Renyuan Xu
- Rafal Weron
- Fred Espen Benth
Citations in the corpus
- Recent advances in reinforcement learning in finance (2021, background): “Instead of profiting from identifying the correct pricemovement direction, the objective of amarketmaker is to profit from earning the bid–ask spread without accumulating undesirably large positions (known as inventory) (Guéant et al., 2012).”
- Enhancing trading strategies with order book signals (2018, background): “See Guilbaud and Pham (2013) and Cartea and Jaimungal (2015) for similar inventory control terms, and Cartea et al.”
- Incorporating order-flow into optimal execution (2016, unknown): “And in market making see the early work of [5], and more recently, [10,11,14,22,23], and [15].”