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Systemic liquidity risk, defined by the IMF as "the risk of simultaneous liquidity difficulties at multiple financial institutions", is a key topic in macroprudential policy and financial stress analysis. Specialized models to simulate funding liquidity risk and contagion are available but they require not only banks' bilateral exposures data but also balance sheet data with sufficient granularity, which are hardly a…
In high frequency trading, accurate prediction of Order Flow Imbalance (OFI) is crucial for understanding market dynamics and maintaining liquidity. This paper introduces a hybrid predictive model that combines Vector Auto Regression (VAR) with a simple feedforward neural network (FNN) to forecast OFI and assess trading intensity. The VAR component captures linear dependencies, while residuals are fed into the FNN to…
Classical market-making strategies based on stochastic control, such as the Avellaneda-Stoikov and the Guéant-Lehalle-Fernandez-Tapia (GLFT) extension, provide closed-form quoting rules, but rest on assumptions that break down at realistic microstructure timescales. One of them is that order flow is stationary, while empirical evidence points to the existence of regimes, possibly associated with algorithmic execution…
We develop a continuous-time structural dynamic model to determine the exact insolvency regions of banks arising from the non-linear interaction between liquidity and credit risk. While existing literature predominantly treats these risks in isolation or via reduced-form specifications, we explicitly model the feedback loop where funding shocks and regulatory constraints force balance-sheet adjustments that can lead …
In this paper, we assume that the permanent market impact of metaorders is linear and that the price is a martingale. Those two hypotheses enable us to derive the evolution of the price from the dynamics of the flow of market orders. For example, if the market order flow is assumed to follow a nearly unstable Hawkes process, we retrieve the apparent long memory of the flow together with a power law impact function wh…
Bilateral CVA as currently implement has the counterintuitive effect of profiting from one's own widening CDS spreads, i.e. increased risk of default, in practice. The unified picture of CVA and liquidity introduced by Morini & Prampolini 2010 has contributed to understanding this. However, there are two significant omissions for practical implementation that come from the same source, i.e. positions not booked in us…
Automated market makers (AMMs) are a cornerstone of decentralised finance (DeFi). Constant product markets with concentrated liquidity, such as UniswapV3, are now a well-established design. In these markets, liquidity providers (LPs) face a sequential decision problem: they must decide when to rebalance their positions and which price ranges to allocate capital to as market conditions evolve. We formulate dynamic liq…
Agent-based models of markets readily produce emergent instabilities, but telling a genuine collective effect apart from a parameter artefact takes discipline. We apply Bouchaud's phase-diagram method to a continuous-double-auction order-book model. The method is to map the full phase diagram, test its robustness to rule changes, and rule out degenerate and numerical origins before we call any feature a tipping point…
We show that net demand for liquidity by algo strategies is identifiable from its trade and price history alone, with no knowledge of its signal or optimization problem. An exact multi-period regret decomposition implies that the sign of this statistic classifies a linear strategy as a net liquidity consumer or provider, recovering the Kyle (1985) informed-trader/market-maker dichotomy from observables alone. Under a…
This paper develops a robust mathematical framework for Constant Function Market Makers (CFMMs) by transitioning from traditional token reserve analyses to a coordinate system defined by price and intrinsic liquidity. We establish a canonical parametrization of the bonding curve that ensures dimensional consistency across diverse trading functions, such as those employed by Uniswap and Balancer, and demonstrate that …
We introduce a structural framework for the geometry of financial order books in which liquidity, supply, and demand are treated as emergent observables rather than primitive market variables. The market is modeled as a relational substrate without assumed metric, temporal, or price coordinates. Observable quantities arise only through observation, implemented here as a reduction of relational degrees of freedom foll…
We study the problem of optimal liquidity withdrawal for a representative liquidity provider (LP) in an automated market maker (AMM). LPs earn fees from trading activity but are exposed to impermanent loss (IL) due to price fluctuations. While existing work has focused on static provision and exogenous exit strategies, we characterise the optimal exit time as the solution to a stochastic control problem with an endog…
Modern economic systems face unprecedented socioeconomic challenges, making systemic resilience and effective liquidity flow management essential. Traditional models such as CAPM, VaR, and GARCH often fail to reflect real market fluctuations and extreme events. This study develops and validates an innovative mathematical model based on the Navier-Stokes equations, aimed at the quantitative assessment, forecasting, an…
This paper applies deep reinforcement learning (DRL) to optimize liquidity provisioning in Uniswap v3, a decentralized finance (DeFi) protocol implementing an automated market maker (AMM) model with concentrated liquidity. We model the liquidity provision task as a Markov Decision Process (MDP) and train an active liquidity provider (LP) agent using the Proximal Policy Optimization (PPO) algorithm. The agent dynamica…
This paper introduces a new algorithmic execution model that integrates interbank limit and market orders with internal liquidity generated through market making. Based on the Cartea et al.\cite{cartea2015algorithmic} framework, we incorporate market impact in interbank orders while excluding it for internal market-making transactions. Our model aims to optimize the balance between interbank and internal liquidity, r…
Portfolio management is an important yet challenging task in AI for FinTech, which aims to allocate investors' budgets among different assets to balance the risk and return of an investment. In this study, we propose a general Multi-objectIve framework with controLLable rIsk for pOrtfolio maNagement (MILLION), which consists of two main phases, i.e., return-related maximization and risk control. Specifically, in the …
We study how trading fees and continuous-time arbitrage affect the profitability of liquidity providers (LPs) in Geometric Mean Market Makers (G3Ms). We use stochastic reflected diffusion processes to analyze the dynamics of a G3M model under the arbitrage-driven market. Our research focuses on calculating LP wealth and extends the findings of Tassy and White related to the constant product market maker (Uniswap v2) …
To assign a value to a portfolio, it is common to use Mark-to-Market prices. However, how should one proceed when the securities are illiquid? When transaction prices are scarce, how can one use all the available real-time information? In this article, we address these questions for over-the-counter (OTC) markets based on requests for quotes (RFQs). We extend the concept of micro-price, which was recently introduced …