Essay on Market Liquidity and Financial Stability

Essay 1: Self-affine, long-memory and market stability - The purpose of this paper is to evaluate the liquidity conditions of financial markets. Drawing inspiration from fractal analysis, I show that the bid-ask spread follows dynamic patterns consistent with those generated by fractional Brownian motion, a mixed process that reflects both the randomness typical of Brownian motion and the correlated behaviour typical of long-memory processes. The determinants of this correlated behaviour are studied using the empirical wavelet transform (EWT), which identifies three components, while theoretical models identify only two (volatility and risk aversion). Finally, the Lyapunov exponent is used to evaluate whether the fractal nature of the bid-ask spread contributes to market stability. The results lead to the conclusion that the bid-ask spread tends toward stability in the medium term, contributing to market stability.