The job of market makers is to provide liquidity to other market participants. The main source of risk for market makers is holding inventory and the uncertainty of future price variation. In many cases, the market makers are in charge of a large range of assets . However, managing the risk in multiple asset cases is an important task. We propose in this paper closed-form approximations for the bid and ask quotes a market maker should set for optimally managing the risk of his/her multi-asset market making book. Our work is an extension of the paper "Optimal market making" by Gu\'eant. We also consider generalizations with asymmetric arrival rate intensities. Moreover, we consider the case where the reference price is modeled with a drift and adverse selection .
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. Furthermore, we propose a perturbative approach to improve our closed-form approximations through Monte-Carlo simulations .
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The job of market makers is to provide liquidity to other market participants. The main source of risk for market makers is holding inventory and the uncertainty of future price variation. In many cases, the market makers are in charge of a large range of assets . However, managing the risk in multiple asset cases is an important task. We propose in this paper
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
R
bid and ask quotes a market maker should set for optimally managing the risk of his/her
value functions of many
R
market making book. Our work is an extension of the paper "Optimal market making" by Gu\'eant. We also consider generalizations with asymmetric arrival rate intensities. Moreover, we consider the case where the reference price is modeled with a drift and adverse selection
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. Furthermore, we propose a perturbative approach to improve our closed-form approximations through Monte-Carlo simulations