Arbitrage Strategy

Liquidity provision of utility indifference type in decentralized exchanges ArXiv ID: 2502.01931 “View on arXiv” Authors: Unknown Abstract We present a mathematical formulation of liquidity provision in decentralized exchanges. We focus on constant function market makers of utility indifference type, which include constant product market makers with concentrated liquidity as a special case. First, we examine no-arbitrage conditions for a liquidity pool and compute an optimal arbitrage strategy when there is an external liquid market. Second, we show that liquidity provision suffers from impermanent loss unless a transaction fee is levied under the general framework with concentrated liquidity. Third, we establish the well-definedness of arbitrage-free reserve processes of a liquidity pool in continuous-time and show that there is no loss-versus-rebalancing under a nonzero fee if the external market price is continuous. We then argue that liquidity provision by multiple liquidity providers can be understood as liquidity provision by a representative liquidity provider, meaning that the analysis boils down to that for a single liquidity provider. Last, but not least, we give an answer to the fundamental question in which sense the very construction of constant function market makers with concentrated liquidity in the popular platform Uniswap v3 is optimal. ...

NYSE Price Correlations Are Abitrageable Over Hours and Predictable Over Years ArXiv ID: 2305.08241 “View on arXiv” Authors: Unknown Abstract Trade prices of about 1000 New York Stock Exchange-listed stocks are studied at one-minute time resolution over the continuous five year period 2018–2022. For each stock, in dollar-volume-weighted transaction time, the discrepancy from a Brownian-motion martingale is measured on timescales of minutes to several days. The result is well fit by a power-law shot-noise (or Gaussian) process with Hurst exponent 0.465, that is, slightly mean-reverting. As a check, we execute an arbitrage strategy on simulated Hurst-exponent data, and a comparable strategy in backtesting on the actual data, obtaining similar results (annualized returns $\sim 60$% if zero transaction costs). Next examining the cross-correlation structure of the $\sim 1000$ stocks, we find that, counterintuitively, correlations increase with time lag in the range studied. We show that this behavior that can be quantitatively explained if the mean-reverting Hurst component of each stock is uncorrelated, i.e., does not share that stock’s overall correlation with other stocks. Overall, we find that $\approx 45$% of a stock’s 1-hour returns variance is explained by its particular correlations to other stocks, but that most of this is simply explained by the movement of all stocks together. Unexpectedly, the fraction of variance explained is greatest when price volatility is high, for example during COVID-19 year 2020. An arbitrage strategy with cross-correlations does significantly better than without (annualized returns $\sim 100$% if zero transaction costs). Measured correlations from any single year in 2018–2022 are about equally good in predicting all the other years, indicating that an overall correlation structure is persistent over the whole period. ...