Related papers: Impermanent loss and loss-vs-rebalancing I: some s…
This paper examines the relationship between impermanent loss (IL) and loss-versus-rebalancing (LVR) in automated market makers (AMMs). Our main focus is on statistical properties, the impact of fees, the role of block times, and, related…
Although modern blockchains almost universally produce blocks at fixed intervals, existing models still lack an analytical formula for the loss-versus-rebalancing (LVR) incurred by Automated Market Makers (AMMs) liquidity providers in this…
Automated Market Makers (AMMs) hold assets and are constantly being rebalanced by external arbitrageurs to match external market prices. Loss-versus-rebalancing (LVR) is a pivotal metric for measuring how an AMM pool performs for its…
We consider the market microstructure of automated market makers (AMMs) from the perspective of liquidity providers (LPs). Our central contribution is a ``Black-Scholes formula for AMMs''. We identify the main adverse selection cost…
We derive the arbitrage gains or, equivalently, Loss Versus Rebalancing (LVR) for arbitrage between \textit{two imperfectly liquid} markets, extending prior work that assumes the existence of an infinitely liquid reference market. Our…
This paper mathematically models a constant-function automated market maker (CFAMM) position as a portfolio of exotic options, known as perpetual American continuous-installment (CI) options. This model replicates an AMM position's delta at…
With the emergence of decentralized finance, new trading mechanisms called Automated Market Makers have appeared. The most popular Automated Market Makers are Constant Function Market Makers. They have been studied both theoretically and…
We design a prediction market to recover a complete and fully general probability distribution over a random variable. Traders buy and sell interval securities that pay \$1 if the outcome falls into an interval and \$0 otherwise. Our market…
Ensuring sufficient liquidity is one of the key challenges for designers of prediction markets. Various market making algorithms have been proposed in the literature and deployed in practice, but there has been little effort to evaluate…
In this paper we examine the relation between market returns and volatility measures through machine learning methods in a high-frequency environment. We implement a minute-by-minute rolling window intraday estimation method using two…
In this article we consider an optimization problem of expected utility maximization of continuous-time trading in a financial market. This trading is constrained by a benchmark for a utility-based shortfall risk measure. The market…
Revisiting the continuous-time Mean-Variance (MV) Portfolio Optimization problem, we model the market dynamics with a jump-diffusion process and apply Reinforcement Learning (RL) techniques to facilitate informed exploration within the…
We propose new nonparametric estimators of the integrated volatility of an It\^{o} semimartingale observed at discrete times on a fixed time interval with mesh of the observation grid shrinking to zero. The proposed estimators achieve the…
Level-based and share-based loss functions are asymptotically equivalent if, in the limit, their averages converge almost surely to a constant ratio. These loss functions take a target value and its realization as arguments and are often…
Stock prices are observed to be random walks in time despite a strong, long term memory in the signs of trades (buys or sells). Lillo and Farmer have recently suggested that these correlations are compensated by opposite long ranged…
We inspect how accurate machine learning (ML) is at forecasting realized variance of the Dow Jones Industrial Average index constituents. We compare several ML algorithms, including regularization, regression trees, and neural networks, to…
In this comment we discuss the problem of reconciling the linear efficiency of price returns with the long-memory of supply and demand. We present new evidence that shows that efficiency is maintained by a liquidity imbalance that co-moves…
We consider the parametric estimation of the volatility and jump activity in a stable Cox-Ingersoll-Ross ($\alpha$-stable CIR) model driven by a standard Brownian Motion and a non-symmetric stable L\'evy process with jump activity $\alpha…
We consider logistic regression including two sets of discrete or categorical covariates that are missing at random (MAR) separately or simultaneously. We examine the asymptotic properties of two multiple imputation (MI) estimators, given…
We develop a novel approach to tackle the common but challenging problem of conformal inference for missing data in machine learning, focusing on Missing at Random (MAR) data. We propose a new procedure Conformal prediction for Missing data…