Automated Market Making: the case of Pegged Assets

TL;DR

This paper introduces a new modeling framework for exchange rates between related cryptoassets using nested Ornstein-Uhlenbeck processes, enabling more accurate AMM design and improved liquidity management for pegged assets.

Contribution

It develops a novel multi-level nested OU process model and an AMM tailored for closely linked cryptoassets, enhancing risk management and liquidity.

Findings

Model accurately captures exchange rate dynamics.

Numerical simulations show efficient quoting for real-world pairs.

Potential to significantly improve liquidity in pegged asset markets.

Abstract

In this paper, we introduce a novel framework to model the exchange rate dynamics between two intrinsically linked cryptoassets, such as stablecoins pegged to the same fiat currency or a liquid staking token and its associated native token. Our approach employs multi-level nested Ornstein-Uhlenbeck (OU) processes, for which we derive key properties and develop calibration and filtering techniques. Then, we design an automated market maker (AMM) model specifically tailored for the swapping of closely related cryptoassets. Distinct from existing models, our AMM leverages the unique exchange rate dynamics provided by the multi-level nested OU processes, enabling more precise risk management and enhanced liquidity provision. We validate the model through numerical simulations using real-world data for the USDC/USDT and wstETH/WETH pairs, demonstrating that it consistently yields efficient quotes. This approach offers significant potential to improve liquidity in markets for pegged assets.