Arbitrage with bounded Liquidity

TL;DR

This paper analyzes arbitrage opportunities between two markets with limited liquidity, deriving the potential gains and losses based on their relative liquidity and trading volumes, considering quadratic trading costs.

Contribution

It extends previous models by accounting for imperfect liquidity in both markets, providing a more realistic assessment of arbitrage gains.

Findings

LVR depends on relative liquidity and trading volume

Arbitrage gains are affected by quadratic trading costs

Model applicable to markets with limited liquidity

Abstract

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.