Arbitrage with bounded Liquidity

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 result highlights that the LVR depends on the relative liquidity and relative trading volume of the two markets between which arbitrage gains are extracted. Our model assumes that trading costs on at least one of the markets is quadratic. This assumption holds well in practice, with the exception of highly liquid major pairs on centralized exchanges, for which we discuss extensions to other cost functions.