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Statistical arbitrage in jump-diffusion models with compound Poisson processes

Author

Listed:
  • Erdinc Akyildirim

    (University of Zurich, Department of Banking and Finance
    Department of Mathematics
    Burdur Mehmet Akif Ersoy University)

  • Frank J. Fabozzi

    (EDHEC Business School)

  • Ahmet Goncu

    (Department of Financial Mathematics)

  • Ahmet Sensoy

    (Faculty of Business Administration)

Abstract

We prove the existence of statistical arbitrage opportunities for jump-diffusion models of stock prices when the jump-size distribution is assumed to have finite moments. We show that to obtain statistical arbitrage, the risky asset holding must go to zero in time. Existence of statistical arbitrage is demonstrated via ‘buy-and-hold until barrier’ and ‘short until barrier’ strategies with both single and double barrier. In order to exploit statistical arbitrage opportunities, the investor needs to have a good approximation of the physical probability measure and the drift of the stochastic process for a given asset.

Suggested Citation

  • Erdinc Akyildirim & Frank J. Fabozzi & Ahmet Goncu & Ahmet Sensoy, 2022. "Statistical arbitrage in jump-diffusion models with compound Poisson processes," Annals of Operations Research, Springer, vol. 313(2), pages 1357-1371, June.
    • Handle: RePEc:spr:annopr:v:313:y:2022:i:2:d:10.1007_s10479-021-03965-w
    DOI: 10.1007/s10479-021-03965-w
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    References listed on IDEAS

    as
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    More about this item

    Keywords

    Statistical arbitrage; Jump-diffusion model; Compound Poisson process; Monte Carlo simulation;
    All these keywords.

    JEL classification:

    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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