Closed-form approximations in multi-asset market making

Philippe Bergault, David Evangelista, Olivier Gu\'eant and Douglas Vieira

Abstract: A large proportion of market making models derive from the seminal model of Avellaneda and Stoikov. The numerical approximation of the value function and the optimal quotes in these models remains a challenge when the number of assets is large. In this article, we propose closed-form approximations for the value functions of many multi-asset extensions of the Avellaneda-Stoikov model. These approximations or proxies can be used (i) as heuristic evaluation functions, (ii) as initial value functions in reinforcement learning algorithms, and/or (iii) directly to design quoting strategies through a greedy approach. Regarding the latter, our results lead to new and easily interpretable closed-form approximations for the optimal quotes, both in the finite-horizon case and in the asymptotic (ergodic) regime.

Date: 2018-10, Revised 2022-09
New Economics Papers: this item is included in nep-mst
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Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:1810.04383

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