Closed-form approximations in multi-asset market making

TL;DR

This paper introduces closed-form approximations for multi-asset market making models based on Avellaneda and Stoikov's framework, enabling efficient computation and strategy design for large asset portfolios.

Contribution

It provides novel closed-form approximations for value functions and optimal quotes in multi-asset market making models, simplifying computations and strategy development.

Findings

Closed-form approximations for value functions in multi-asset models

New explicit formulas for optimal quotes in finite and ergodic regimes

Approximations useful for heuristics, reinforcement learning, and strategy design

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.