arXiv · arXiv q-fin · 2026
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 …
Nader Karimi, Davood Ahmadian
arXiv · arXiv q-fin · 2024
We develop a liquidity-sensitive multivariate volatility framework to improve the estimation of time-varying covariance structures under market frictions. We introduce two novel portfolio-level liquidity measures, liquidity jump and liquidity diffusion, which capture magnitude and volatility of liquidity fluctuation, respectively, and construct liquidity-adjusted return and volatility that reflect real-time liquidity…
Qi Deng
arXiv · arXiv q-fin · 2023
Constant product markets with concentrated liquidity (CL) are the most popular type of automated market makers. In this paper, we characterise the continuous-time wealth dynamics of strategic LPs who dynamically adjust their range of liquidity provision in CL pools. Their wealth results from fee income, the value of their holdings in the pool, and rebalancing costs. Next, we derive a self-financing and closed-form op…
Álvaro Cartea, Fayçal Drissi, Marcello Monga
arXiv · arXiv · 2021
This article is part of a comprehensive research project on liquidity risk in asset management, which can be divided into three dimensions. The first dimension covers the modeling of the liability liquidity risk (or funding liquidity), the second dimension is dedicated to the modeling of the asset liquidity risk (or market liquidity), whereas the third dimension considers the management of the asset-liability liquidi…
Thierry Roncalli
arXiv · arXiv · 2021
This article is part of a comprehensive research project on liquidity risk in asset management, which can be divided into three dimensions. The first dimension covers liability liquidity risk (or funding liquidity) modeling, the second dimension focuses on asset liquidity risk (or market liquidity) modeling, and the third dimension considers the asset-liability management of the liquidity gap risk (or asset-liability…
Thierry Roncalli, Amina Cherief, Fatma Karray-Meziou, Margaux Regnault
arXiv · arXiv · 2021
This article is part of a comprehensive research project on liquidity risk in asset management, which can be divided into three dimensions. The first dimension covers liability liquidity risk (or funding liquidity) modeling, the second dimension focuses on asset liquidity risk (or market liquidity) modeling, and the third dimension considers asset-liability liquidity risk management (or asset-liability matching). The…
Thierry Roncalli, Fatma Karray-Meziou, François Pan, Margaux Regnault
arXiv · arXiv q-fin · 2019
Price impact of a trade is an important element in pre-trade and post-trade analyses. We introduce a framework to analyze the market price of liquidity risk, which allows us to derive an inhomogeneous Bernoulli ordinary differential equation. We obtain two closed form solutions, one of which reproduces the linear function of the order flow in Kyle (1985) for informed traders. However, when traders are not as asymmetr…
Masaaki Kijima, Christopher Ting
arXiv · arXiv · 2019
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…
V. Macchiati, G. Brandi, G. Cimini, G. Caldarelli, D. Paolotti
arXiv · arXiv q-fin · 2018
We study a continuous-time version of the intermediation model of Grossman and Miller (1988). To wit, we solve for the competitive equilibrium prices at which liquidity takers' demands are absorbed by dealers with quadratic inventory costs, who can in turn gradually transfer these positions to an exogenous open market with finite liquidity. This endogenously leads to transient price impact in the dealer market. Smoot…
Peter Bank, Ibrahim Ekren, Johannes Muhle-Karbe
arXiv · arXiv q-fin · 2016
We present a simulation-and-regression method for solving dynamic portfolio allocation problems in the presence of general transaction costs, liquidity costs and market impacts. This method extends the classical least squares Monte Carlo algorithm to incorporate switching costs, corresponding to transaction costs and transient liquidity costs, as well as multiple endogenous state variables, namely the portfolio value…
Rongju Zhang, Nicolas Langrené, Yu Tian, Zili Zhu, Fima Klebaner
arXiv · arXiv q-fin · 2015
In this article, we present a discrete time modeling framework, in which the shape and dynamics of a Limit Order Book (LOB) arise endogenously from an equilibrium between multiple market participants (agents). We use the proposed modeling framework to analyze the effects of trading frequency on market liquidity in a very general setting. In particular, we demonstrate the dual effect of high trading frequency. On the …
Roman Gayduk, Sergey Nadtochiy
arXiv · arXiv · 2012
We propose a unified structural credit risk model incorporating both insolvency and illiquidity risks, in order to investigate how a firm's default probability depends on the liquidity risk associated with its financing structure. We assume the firm finances its risky assets by mainly issuing short- and long-term debt. Short-term debt can have either a discrete or a more realistic staggered tenor structure. At rollov…
Gechun Liang, Eva Lütkebohmert, Wei Wei
arXiv · arXiv · 2026
We present SAiFE_gym, a Python module that provides a collection of simulation environments for studying trading problems in Constant Product Markets (CPMs) with Concentrated Liquidity (CL). These markets give Liquidity Providers (LPs) granular control over how their capital is allocated and enable them to adjust their range of liquidity provision dynamically based on market conditions, which in turn, dictates how th…
Georgios Chionas, Charalampos Kleitsikas, Stefanos Leonardos, Leandro Sánchez-Betancourt, Carmine Ventre
arXiv · arXiv · 2026
Loss-versus-Rebalancing (LVR) is the dominant adverse-selection cost borne by liquidity providers on automated market makers. Under geometric Brownian motion, arbitrage profit scales with the probability of a profitable block, which vanishes as the block time $Δt \to 0$; this is the standing argument for ever-shorter blocks. Modeling the reference price instead as a jump-diffusion, I show that the constant-product LV…
Nils Bundi
arXiv · arXiv · 2026
Automated Market Makers based on concentrated liquidity, such as Uniswap v3, significantly improve capital efficiency but expose Liquidity Providers (LPs) to adverse selection costs, formalized as Loss-Versus-Rebalancing (LVR). While theoretical literature quantifies these costs, the interplay between realistic blockchain microstructure and endogenous pricing mechanisms remains under-explored. This paper develops a g…
Daniele Maria Di Nosse, Fabrizio Lillo
arXiv · arXiv · 2020
Before the 2008 financial crisis, most research in financial mathematics focused on pricing options without considering the effects of counterparties' defaults, illiquidity problems, and the role of the sale and repurchase agreement (Repo) market. Recently, models were proposed to address this by computing a total valuation adjustment (XVA) of derivatives; however without considering a potential crisis in the market.…
Weijie Pang, Stephan Sturm
OpenAlex · Review of Financial Studies · 2012 · cites 565
Order flow is toxic when it adversely selects market makers, who may be unaware they are providing liquidity at a loss. We present a new procedure to estimate flow toxicity based on volume imbalance and trade intensity (the VPIN toxicity metric). VPIN is updated in volume time, making it applicable to the high-frequency world, and it does not require the intermediate estimation of non-observable parameters or the app…
David Easley, Marcos López de Prado, Maureen O’Hara
OpenAlex · Review of Financial Studies · 2008 · cites 5059
We provide a model that links an asset's market liquidity (i.e., the ease with which it is traded) and traders' funding liquidity (i.e., the ease with which they can obtain funding). Traders provide market liquidity, and their ability to do so depends on their availability of funding. Conversely, traders' funding, i.e., their capital and margin requirements, depends on the assets' market liquidity. We show that, unde…
Markus K. Brunnermeier, Lasse Heje Pedersen