Models of Market Liquidity: Applications to Traditional Markets and Automated Market Makers

Abstract

The thesis studies algorithmic trading problems for liquidity takers (LTs) and liquidity providers (LPs) in traditional electronic markets and in decentralised trading platforms that use Automated Market Makers (AMMs). AMMs are a new paradigm in the design of trading venues and are based on liquidity pooling. Chapter 1 introduces the literature on algorithmic trading in traditional markets. Chapter 2 solves a multi-asset optimal trading problem in LOBs where the agent adopts a CARA utility and the prices follow multivariate Ornstein-Uhlenbeck dynamics. These dynamics account for the presence of cointegration between the assets’ prices. We showcase the use of the model to enhance the performance of portfolio execution programmes and to build statistical arbitrage strategies using data from the Equity and FX markets. Chapter 3 uses stochastic control tools to solve a general differential Riccati equation (DRE) with an indefinite quadratic coefficient. We use the result to provide solutions to two algorithmic portfolio trading problems; one is optimal trading in LOBs with Bayesian learning of the drift using signals and past prices, the second is multi-asset market making in OTC markets with three important features: (𝑖) dynamics that incorporate cointegration and predictive signals, (𝑖𝑖) external hedging and client tiering, and (𝑖𝑖𝑖) computationally efficient methods to obtain quotes for large portfolios. Chapter 4 introduces AMMs and describes how liquidity takers and providers interact in liquidity pools. Chapter 5 studies optimal execution in a constant function market maker (CFMM), a popular type of AMMs. In particular, we use the convexity of the trading function as an approximation for the execution costs incurred by LTs. Chapter 6 introduces a new comprehensive metric of predictable loss (PL) for LPs in CFMMs. PL compares the value of the LP’s holdings in the liquidity pool with that of a self-financing portfolio that replicates the LP’s holdings and invests in a risk-free account. We show that the losses stem from two sources: the convexity cost, which depends on liquidity taking activity and the convexity of the pool’s trading function; the opportunity cost, which is due to locking the LP’s assets in the pool. Finally, Chapter 7 derives continuous-time dynamics for the wealth of LPs and provides a closed-form dynamic liquidity provision strategy in constant product market makers (CPMMs) with concentrated liquidity. The strategy dynamically adjusts the liquidity range around the exchange rate as a function of market trend, volatility, and liquidity taking activity in the pool. We prove that the profitability of liquidity provision depends on the tradeoff between PL and fee income. Chapter 5, 6, and 7 use Uniswap v3 data to showcase the superior out-of-sample performance of our strategies.

Keywords: Optimal Execution, Market Making, Decentralised Finance, Automated Market Making, Algorithmic Trading, Statistical Arbitrage, Predictive Signals, Market Impact