Closed-form Approximations in Multi-asset Market Making

Philippe Bergault, Olivier Guéant, David Evangelista and Douglas Vieira
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Philippe Bergault: CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique
David Evangelista: FGV/EMAp - Fundação Getulio Vargas - Escola de Matemática Aplicada [Rio de Janeiro]
Douglas Vieira: Imperial College London

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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.

Keywords: Algorithmic trading; market making; stochastic optimal control; Closed-form approximations; Monte-Carlo methods (search for similar items in EconPapers)
Date: 2021-03-04
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Citations: View citations in EconPapers (11)

Published in Applied Mathematical Finance, 2021, 28 (2), pp.101-142. ⟨10.1080/1350486X.2021.1949359⟩

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Working Paper: Closed-form Approximations in Multi-asset Market Making (2021)
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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-03680074

DOI: 10.1080/1350486X.2021.1949359

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