Abstract
With the rise of electronification and trading automation, the task of quoting assets on many financial markets must be carried out algorithmically by market makers. Market making models and algorithms have therefore been an important research topic in recent years, at the frontier between economics, quantitative finance, scientific computing, and machine learning. The goal of this text is (i) to present a typical multi-asset market making model relevant for most over-the-counter markets, (ii) to show how to use stochastic optimal control tools to derive a theoretical characterization of optimal quotes in that model, and (iii) to discuss the various methods proposed in the literature that could be used in practice in the financial industry for building market making algorithms.
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Notes
- 1.
Intensities are instantaneous probabilities to trade in this context.
- 2.
The probability to trade with a client depends monotonically on the proposed price.
- 3.
It is indeed a system of nonlinear ordinary differential equations because the variable q takes discrete values.
- 4.
For most extensions of the above model, these two problems remain the relevant ones.
References
M. Avellaneda and S. Stoikov. High-frequency trading in a limit order book. Quantitative Finance, 8(3):217–224, 2008.
A. Barzykin, P. Bergault, and O. Guéant. Algorithmic market making in foreign exchange cash markets with hedging and market impact. Working paper, 2021.
A. Barzykin, P. Bergault, and O. Guéant. Market making by an FX dealer: tiers, pricing ladders and hedging rates for optimal risk control. Working paper, 2022.
P. Bergault and O. Guéant. Size matters for OTC market makers: general results and dimensionality reduction technique. Mathematical Finance, 31(1):279–322 2020.
P. Bergault, D. Evangelista, O. Guéant, and D. Vieira. Closed-form approximations in multi-asset market making. Applied Mathematical Finance, to appear.
L. Campi and D. Zabaljauregui. Optimal market making under partial information with general intensities. Applied Mathematical Finance 27, 2020.
Á.Cartea, R. Donnelly, and S. Jaimungal. Algorithmic trading with model uncertainty. SIAM Journal on Financial Mathematics, 8(1):635–671, 2017.
Á. Cartea, S. Jaimungal, and J. Penalva. Algorithmic and high-frequency trading. Cambridge University Press, 2015.
Á. Cartea, S. Jaimungal, and J. Ricci. Buy low, sell high: A high frequency trading perspective. SIAM Journal on Financial Mathematics, 5(1):415–444, 2014.
Á. Cartea, S. Jaimungal, and J. Ricci. Algorithmic trading, stochastic control, and mutually exciting processes. SIAM Review, 60(3):673–703, 2018.
O. Guéant. The Financial Mathematics of Market Liquidity: From optimal execution to market making, volume 33. CRC Press, 2016.
O. Guéant. Optimal market making. Applied Mathematical Finance, 24(2):112–154, 2017.
O. Guéant and C.-A. Lehalle. General intensity shapes in optimal liquidation. Mathematical Finance, 25(3):457–495, 2015.
O. Guéant, C.-A. Lehalle, and J. Fernandez-Tapia. Dealing with the inventory risk: a solution to the market making problem. Mathematics and Financial Economics, 7(4):477–507, 2013.
O. Guéant and I. Manziuk. Deep reinforcement learning for market making in corporate bonds: beating the curse of dimensionality. Applied Mathematical Finance, 26(5):387–452, 2019.
Th. Ho and H.R. Stoll. On dealer markets under competition. The Journal of Finance, 35(2):259–267, 1980.
Th. Ho and H.R. Stoll. Optimal dealer pricing under transactions and return uncertainty. Journal of Financial Economics, 9(1):47–73, 1981.
Th. Ho and H.R. Stoll. The dynamics of dealer markets under competition. The Journal of Finance, 38(4):1053–1074, 1983.
P. Jusselin. Optimal market making with persistent order flow. arXiv preprint arXiv:2003.05958, 2020.
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Guéant, O. (2022). Computational Methods for Market Making Algorithms. In: Ehrhardt, M., Günther, M. (eds) Progress in Industrial Mathematics at ECMI 2021. ECMI 2021. Mathematics in Industry(), vol 39. Springer, Cham. https://doi.org/10.1007/978-3-031-11818-0_66
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