Discretization of continuous-time arbitrage strategies in financial markets with fractional Brownian motion

Abstract

This study evaluates the practical usefulness of continuous-time arbitrage strategies designed to exploit serial correlation in fractional financial markets. Specifically, we revisit the strategies of \cite{Shiryaev1998} and \cite{Salopek1998} and transfer them to a real-world setting by distretizing their dynamics and introducing transaction costs. In Monte Carlo simulations with various market and trading parameter settings, we show that both are highly promising with respect to terminal portfolio values and loss probabilities. These features and complementary sparsity make them valuable additions to the toolkit of quantitative investors.