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

Author

Listed:
  • Kerstin Lamert

    (Brandenburg University of Technology Cottbus-Senftenberg)

  • Benjamin R. Auer

    (Friedrich Schiller University Jena
    Department of Finance
    Money and International Finance)

  • Ralf Wunderlich

    (Brandenburg University of Technology Cottbus-Senftenberg)

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.

Suggested Citation

  • Kerstin Lamert & Benjamin R. Auer & Ralf Wunderlich, 2025. "Discretization of continuous-time arbitrage strategies in financial markets with fractional Brownian motion," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 101(2), pages 163-218, April.
    • Handle: RePEc:spr:mathme:v:101:y:2025:i:2:d:10.1007_s00186-025-00889-0
    DOI: 10.1007/s00186-025-00889-0
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    More about this item

    Keywords

    Arbitrage strategies; Fractional Brownian motion; Fractional Black–Scholes model; Serial correlation; Simulation;
    All these keywords.

    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G17 - Financial Economics - - General Financial Markets - - - Financial Forecasting and Simulation

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