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

Kerstin Lamert (), Benjamin R. Auer () and Ralf Wunderlich ()
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Kerstin Lamert: Brandenburg University of Technology Cottbus-Senftenberg
Benjamin R. Auer: Friedrich Schiller University Jena
Ralf Wunderlich: Brandenburg University of Technology Cottbus-Senftenberg

Mathematical Methods of Operations Research, 2025, vol. 101, issue 2, No 2, 163-218

Abstract: 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 Shiryaev (On arbitrage and replication for fractal models, 1998) and Salopek (Stoch Process Appl 76:217–230, 1998) 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 as well as a formal analysis of discretization error, we show that both are promising with respect to terminal portfolio values and loss probabilities. These features and complementary sparsity make them worth serious consideration in the toolkit of quantitative investors.

Keywords: Arbitrage strategies; Fractional Brownian motion; Fractional Black–Scholes model; Serial correlation; Simulation; 91G10; 91G80 (search for similar items in EconPapers)
JEL-codes: G11 G17 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s00186-025-00889-0

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