arXiv · arXiv q-fin · 2010
We study the cascading dynamics immediately before and immediately after 219 market shocks. We define the time of a market shock T_{c} to be the time for which the market volatility V(T_{c}) has a peak that exceeds a predetermined threshold. The cascade of high volatility "aftershocks" triggered by the "main shock" is quantitatively similar to earthquakes and solar flares, which have been described by three empirical…
Alexander M. Petersen, Fengzhong Wang, Shlomo Havlin, H. Eugene Stanley
arXiv · arXiv q-fin · 2026
Three traits of decentralized finance are studied. First, the market impact function is derived for optimal-growth liquidity providers. For a standard random walk, the classic square-root impact is recovered. An extension is then derived to fit general fractional Ornstein-Uhlenbeck processes. These findings break with the linearized liquidity models used in most decentralized exchanges. Second, a Constant Product Mar…
B. K. Meister
arXiv · arXiv q-fin · 2025
Decentralized exchanges (DEXs) face persistent challenges in liquidity retention and user engagement due to inefficiencies in conventional automated market maker (AMM) designs. This work proposes a dual-mechanism framework to address these limitations: a ``Better Market Maker (BMM)'', which is a liquidity-optimized AMM based on a power-law invariant ($X^nY = K$, $n = 4$), and a dynamic rebate system (DRS) for redistr…
CY Yan, Steve Keol, Xo Co, Nate Leung
arXiv · arXiv q-fin · 2024
In decentralized finance, any individual can pool their assets into an automated market maker (AMM) -- herein we focus on the constant product market maker (CPMM) -- in exchange for a claim on a fraction of future pool assets and fees earned from the market making operations. This position is represented by a liquidity token, whose prevailing on-chain price is effectively the initial deposited assets. Though this pri…
Maxim Bichuch, Zachary Feinstein
arXiv · arXiv q-fin · 2024
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) …
Cheuk Yin Lee, Shen-Ning Tung, Tai-Ho Wang
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 q-fin · 2022
The standard approach for compensating liquidity providers on many decentralized exchanges (DEX) for serving as counter-party to swaps is through charging a small percentage of fees. The expected payoff from the cash flow of this mode of market making has yet to be mathematically formulated in terms of volatility in the existing literature. We provide here a preliminary derivation of the payoff formula, by making the…
Jin Hong Kuan
arXiv · arXiv q-fin · 2021
Uniswap is a decentralized exchange (DEX) and was first launched on November 2, 2018 on the Ethereum mainnet [1] and is part of an Ecosystem of products in Decentralized Finance (DeFi). It replaces a traditional order book type of trading common on centralized exchanges (CEX) with a deterministic model that swaps currencies (or tokens/assets) along a fixed price function determined by the amount of currencies supplie…
Andreas A. Aigner, Gurvinder Dhaliwal
arXiv · arXiv q-fin · 2024
Automated market makers (AMMs) are a new type of trading venues which are revolutionising the way market participants interact. At present, the majority of AMMs are constant function market makers (CFMMs) where a deterministic trading function determines how markets are cleared. Within CFMMs, we focus on constant product market makers (CPMMs) which implements the concentrated liquidity (CL) feature. In this thesis we…
Marcello Monga
arXiv · arXiv q-fin · 2023
Automated market makers (AMMs) are a new prototype of decentralised exchanges which are revolutionising market interactions. The majority of AMMs are constant product markets (CPMs) where exchange rates are set by a trading function. This work studies optimal trading and statistical arbitrage in CPMs where balancing exchange rate risk and execution costs is key. Empirical evidence shows that execution costs are accur…
Álvaro Cartea, Fayçal Drissi, Marcello Monga
arXiv · arXiv q-fin · 2021
Automated market makers (AMM) have grown to obtain significant market share within the cryptocurrency ecosystem, resulting in a proliferation of new products pursuing exotic strategies for horizontal differentiation. Yet, their theoretical properties are curiously homogeneous when a set of basic assumptions are met. In this paper, we start by presenting a universal approach to deriving a formula for liquidity provisi…
Johannes Rude Jensen, Mohsen Pourpouneh, Kurt Nielsen, Omri Ross
arXiv · arXiv q-fin · 2020
This paper compares mathematical models for automated market makers including logarithmic market scoring rule (LMSR), liquidity sensitive LMSR (LS-LMSR), constant product/mean/sum, and others. It is shown that though LMSR may not be a good model for Decentralized Finance (DeFi) applications, LS-LMSR has several advantages over constant product/mean based automated market makers. However, LS-LMSR requires complicated …
Yongge Wang
OpenAlex · Journal of Applied Econometrics · 2007 · cites 12224
Abstract A number of panel unit root tests that allow for cross‐section dependence have been proposed in the literature that use orthogonalization type procedures to asymptotically eliminate the cross‐dependence of the series before standard panel unit root tests are applied to the transformed series. In this paper we propose a simple alternative where the standard augmented Dickey–Fuller (ADF) regressions are augmen…
M. Hashem Pesaran
arXiv · arXiv q-fin · 2026
A credit rating of AAA asserts near-certainty of repayment. This paper asks whether the pre-crisis information environment could have supported that assertion for structured products. Bayes' theorem implies that any reliability target requires a minimum level of statistical discrimination between instruments that will repay and those that will not. At structured-finance base rates, a four-nines reliability target dem…
Marco Pollanen
arXiv · arXiv q-fin · 2020
This chapter presents a history of international trade finance - the oldest domain of international finance - from its emergence in the Middle Ages up to today. We describe how the structure and governance of the global trade finance market changed over time and how trade credit instruments evolved. Trade finance products initially consisted of idiosyncratic assets issued by local merchants and bankers. The financing…
Olivier Accominotti, Stefano Ugolini
arXiv · arXiv q-fin · 2015
We consider the problem of optimal trading for a power producer in the context of intraday electricity markets. The aim is to minimize the imbalance cost induced by the random residual demand in electricity, i.e. the consumption from the clients minus the production from renewable energy. For a simple linear price impact model and a quadratic criterion, we explicitly obtain approximate optimal strategies in the intra…
René Aïd, Pierre Gruet, Huyên Pham
arXiv · arXiv q-fin · 2012
Regarding the intraday sequence of high frequency returns of the S&P index as daily realizations of a given stochastic process, we first demonstrate that the scaling properties of the aggregated return distribution can be employed to define a martingale stochastic model which consistently replicates conditioned expectations of the S&P 500 high frequency data in the morning of each trading day. Then, a more general fo…
Fulvio Baldovin, Francesco Camana, Massimiliano Caporin, Michele Caraglio, Attilio L. Stella
arXiv · arXiv q-fin · 2011
We consider a structural credit model for a large portfolio of credit risky assets where the correlation is due to a market factor. By considering the large portfolio limit of this system we show the existence of a density process for the asset values. This density evolves according to a stochastic partial differential equation and we establish existence and uniqueness for the solution taking values in a suitable fun…
Nick Bush, Ben M. Hambly, Helen Haworth, Lei Jin, Christoph Reisinger