arXiv · arXiv q-fin · 2022
This article analytically characterizes the impermanent loss of concentrated liquidity provision for automatic market makers in decentralised markets such as Uniswap. We propose two static replication formulas for the impermanent loss by a combination of European calls or puts with strike prices supported on the liquidity provision price interval. It facilitates liquidity providers to hedge permanent loss by trading …
Jun Deng, Hua Zong, Yun Wang
arXiv · arXiv q-fin · 2015
In this work we introduce the notion of fully incomplete markets. We prove that for these markets the super-replication price coincide with the model free super-replication price. Namely, the knowledge of the model does not reduce the super-replication price. We provide two families of fully incomplete models: stochastic volatility models and rough volatility models. Moreover, we give several computational examples. …
Yan Dolinsky, Ariel Neufeld
arXiv · arXiv · 2026
We study cash-flow forecasting for derivatives used in liquidity management and clarify its relation to risk-neutral valuation and replication. While it is well known that expectations under different measures (e.g., $\mathbb{P}$ vs. $\mathbb{Q}$) can yield different undiscounted cash-flows, further inconsistencies arise when payment times are stochastic. We show that using discounting sensitivities (funding-curve he…
Christian P. Fries
arXiv · arXiv q-fin · 2008
We extend a linear version of the liquidity risk model of Cetin et al. (2004) to allow for price impacts. We show that the impact of a market order on prices depends on the size of the transaction and the level of liquidity. We obtain a simple characterization of self-financing trading strategies and a sufficient condition for no arbitrage. We consider a stochastic volatility model in which the volatility is partly c…
Alexandre F. Roch
arXiv · arXiv q-fin · 2025
In response to growing demand for resilient and transparent financial instruments, we introduce a novel framework for replicating private equity (PE) performance using liquid, AI-enhanced strategies. Despite historically delivering robust returns, private equity's inherent illiquidity and lack of transparency raise significant concerns regarding investor trust and systemic stability, particularly in periods of height…
E. Benhamou, JJ. Ohana, B. Guez, E. Setrouk, T. Jacquot
arXiv · arXiv · 2026
Portfolio replication, or the construction of a tradable basket of assets to match the risk-return profile of a target benchmark, is fundamentally an ill-posed inverse problem. When restricted to a subset of available assets, classical variance-minimizing models often yield unstable, over-leveraged portfolios highly vulnerable to market shocks. We propose a unified, two-stage methodology rooted in information theory …
Argimiro Arratia, Henryk Gzyl
arXiv · arXiv · 2026
This study strengthens the foundations of multi-venue market modeling by attempting an independent replication of Wah and Wellman's 2016 model of latency arbitrage in a fragmented market. We find that faithful replication is hindered by missing implementation details in the original paper and limited quantitative reporting. We demonstrate that increasing the number of simulation runs beyond the original design allows…
Ethan Ratliff-Crain, Colin M. Van Oort, Matthew T. K. Koehler, Brian F. Tivnan
arXiv · arXiv · 2025
This work analytically characterizes impermanent loss for automated market makers (AMMs) in decentralized markets such as Uniswap or Balancer (CPMM). We derive a static replication formula for the pool's value using a combination of European calls and puts. Furthermore, we establish a result guaranteeing hedging coverage for all final prices within a predefined interval. These theoretical results motivate a numerical…
Agustin Muñoz Gonzalez, Juan Ignacio Sequeira, Ariel Dembling
arXiv · arXiv · 2022
We present a semi-static hedging algorithm for callable interest rate derivatives under an affine, multi-factor term-structure model. With a traditional dynamic hedge, the replication portfolio needs to be updated continuously through time as the market moves. In contrast, we propose a semi-static hedge that needs rebalancing on just a finite number of instances. We show, taking as an example Bermudan swaptions, that…
Jori Hoencamp, Shashi Jain, Drona Kandhai
arXiv · arXiv · 2015
Since Hobson's seminal paper [D. Hobson: Robust hedging of the lookback option. In: Finance Stoch. (1998)] the connection between model-independent pricing and the Skorokhod embedding problem has been a driving force in robust finance. We establish a general pricing-hedging duality for financial derivatives which are susceptible to the Skorokhod approach. Using Vovk's approach to mathematical finance we derive a mode…
Mathias Beiglböck, Alexander M. G. Cox, Martin Huesmann, Nicolas Perkowski, David J. Prömel
arXiv · arXiv q-fin · 2025
We study the economic viability of liquidity provision in decentralised exchanges (DEXs) within a structural framework in which market outcomes are endogenous. We formulate strategic interactions as a sequential game: a risk-averse liquidity provider (LP) sets the supply of liquidity in the DEX and a costly dynamic replication strategy in a centralised exchange (CEX), price-sensitive traders determine trading volumes…
Fayçal Drissi, Xuchen Wu, Sebastian Jaimungal
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 · 2025
Commodity Trading Advisors (CTAs) have historically relied on trend-following rules that operate on vastly different horizons from long-term breakouts that capture major directional moves to short-term momentum signals that thrive in fast-moving markets. Despite a large body of work on trend following, the relative merits and interactions of short-versus long-term trend systems remain controversial. This paper adds t…
Eric Benhamou, Jean-Jacques Ohana, Alban Etienne, Béatrice Guez, Ethan Setrouk
arXiv · arXiv · 2025
This study replicates the findings of Wang et al. (2017) on reference-dependent preferences and their impact on the risk-return trade-off in the Chinese stock market, a unique context characterized by high retail investor participation, speculative trading behavior, and regulatory complexities. Capital Gains Overhang (CGO), a proxy for unrealized gains or losses, is employed to explore how behavioral biases shape cro…
Penggan Xu
arXiv · arXiv · 2023
The Black-Scholes-Merton model is a mathematical model for the dynamics of a financial market that includes derivative investment instruments, and its formula provides a theoretical price estimate of European-style options. The model's fundamental idea is to eliminate risk by hedging the option by purchasing and selling the underlying asset in a specific way, that is, to replicate the payoff of the option with a port…
Tongseok Lim
arXiv · arXiv · 2018
This paper derives a robust on-line equity trading algorithm that achieves the greatest possible percentage of the final wealth of the best pairs rebalancing rule in hindsight. A pairs rebalancing rule chooses some pair of stocks in the market and then perpetually executes rebalancing trades so as to maintain a target fraction of wealth in each of the two. After each discrete market fluctuation, a pairs rebalancing r…
Alex Garivaltis
arXiv · arXiv · 2025
We study opportunistic optimal liquidation over fixed deadlines on BTC-USD limit-order books (LOB). We present RL-Exec, a PPO agent trained on historical replays augmented with endogenous transient impact (resilience), partial fills, maker/taker fees, and latency. The policy observes depth-20 LOB features plus microstructure indicators and acts under a sell-only inventory constraint to reach a residual target. Evalua…
Enzo Duflot, Stanislas Robineau
arXiv · arXiv · 2025
Transaction costs and regime shifts are major reasons why paper portfolios fail in live trading. We introduce FR-LUX (Friction-aware, Regime-conditioned Learning under eXecution costs), a reinforcement learning framework that learns after-cost trading policies and remains robust across volatility-liquidity regimes. FR-LUX integrates three ingredients: (i) a microstructure-consistent execution model combining proporti…
Jian'an Zhang