Closed-form Approximations in Multi-asset Market Making

Philippe Bergault, David Evangelista, Olivier Guéant and Douglas Vieira

Applied Mathematical Finance, 2021, vol. 28, issue 2, 101-142

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: 2021
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Working Paper: Closed-form Approximations in Multi-asset Market Making (2021)
Working Paper: Closed-form Approximations in Multi-asset Market Making (2021)
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DOI: 10.1080/1350486X.2021.1949359

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