Seminarium z udziałem Bartosza Bieganowskiego – 27 kwietnia

27 kwietnia o godzinie 18:30 odbędzie się seminarium organizowane wspólnie przez Quantitative Finance Research Group (QFRG WNE UW) oraz DSLab WNE UW. Tym razem Bartosz Bieganowski, związany z Katedrą Finansów Ilościowych i Uczenia Maszynowego WNE, zaprezentuje wyniki badania przeprowadzonego wraz z dr. hab. Robertem Ślepaczukiem, prof. ucz. Badanie zatytułowane jest Optimal Market Making under Exchange Rate Limits. Zapraszamy do zapoznania się z abstraktem - poniżej.

Spotkanie odbędzie się w formie hybrydowej - na Wydziale Nauk Ekonomicznych Uniwersytetu Warszawskiego (ul. Długa 44/50, Warszawa) w sali B002. Istnieje możliwość udziału zdalnego, na platformie Zoom. Prezentacja zagadnienia przewidziana jest na 45 minut, następnie odbędzie się wspólna dyskusja. Uprzejmie prosimy o wcześniejsze przybycie/zalogowanie się na spotkanie.

Link do spotkania zostanie udostępniony po uprzednim napisaniu wiadomości mailowej na adres: 4^Q&y'$6=YaExzSn.~-GkJ]#[!QAqifkrUQP%%pKwnc}P\3

Abstrakt:

Market makers on modern electronic exchanges face a fundamental tension: frequent requoting improves quote positioning but consumes finite rate-limit tokens imposed by the exchange. We model this as a hybrid impulse-control problem within the Avellaneda-Stoikov framework, where the agent optimizes CARA utility subject to a token-bucket constraint on order placements and cancellations. Treating the inaction bandwidth (the maximum tolerable quote drift before repricing) as the central decision variable, we derive a closed-form approximation for the optimal threshold under Poisson fill arrivals: the optimal bandwidth scales as the fourth root of the ratio of volatility to inventory risk and rate-limit cost, yielding a Fourth-Root Law that makes the trade-off between quote staleness and token consumption explicit. We then train a Proximal Policy Optimization (PPO) agent with a structurally symmetric two-phase architecture, enforcing exact bid/ask symmetry by construction rather than by learning, and a continuous tolerance action that maps directly to the theoretical inaction bandwidth. The learned value function serves as a reward forecast, identifying the repricing threshold as the point where expected repositioning gains exceed rate-limit opportunity costs. Sensitivity analysis across a grid of volatility and fill-rate parameters confirms that the agent recovers the qualitative predictions of the closed-form solution: wider spreads and larger inaction bandwidths under high volatility, tighter spreads and more aggressive repricing when fill rates are high. For the multi-asset case with a shared rate-limit pool, we derive an optimal allocation rule where the fraction of tokens devoted to an asset is proportional to the product of its volatility and square root of its fill sensitivity. We then verify that the PPO agent trained on a two-asset environment with heterogeneous parameters converges to this proportional allocation. These results bridge analytical market-making theory, deep reinforcement learning, and technological reality of being a market maker on modern electronic exchanges by offering both interpretable closed-form guidance and an empirically validated RL framework for rate-constrained liquidity provision.

Keywords: large language models, LASSO, SVR, HAR, machine learning, cryptocurrencies, Bitcoin returns, volatility