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Multifractional processes in finance

Author

Listed:
  • Bianchi, Sergio

    (Department of Finance and Risk Engineering, Polytechnic Institute, New York University, New York, USA)

  • Pianese, Augusto

    (Department of Economics and Law, University of Cassino, Cassino, FR, Italy)

Abstract

There is a growing consensus that fundamental financial theory based on the assumption that markets are complete is not sustainable when financial markets become increasingly complex. Traditional models fail to capture many of the stylized facts and biases identified by recent financial developments that have sought to explain financial prices when markets are incomplete. These approaches, and in particular behavioral finance, in turn, do not formalize and quantify the assumptions their approaches are based on, which are required for financial calculations and assets pricing. One of the open questions is therefore whether a model exists that is able to deduce the overall equilibrium stated by the current paradigm as a sequence of balancing disequilibria. To this aim, a class of stochastic models – the multifractional processes – is suggested and presented in this paper. Multifractional processes are defined as a generalization of fractional Brownian motion, providing a parsimonious mechanisms for modeling real financial markets. This approach includes temporary departures from equilibrium triggered by investors’ biases.

Suggested Citation

  • Bianchi, Sergio & Pianese, Augusto, 2014. "Multifractional processes in finance," Risk and Decision Analysis, IOS Press, issue 5, pages 1-22.
    • Handle: RePEc:ris:iosrda:0001
    as

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    Citations

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    Cited by:

    1. Sergio Bianchi & Massimiliano Frezza, 2018. "Liquidity, Efficiency and the 2007-2008 Global Financial Crisis," Annals of Economics and Finance, Society for AEF, vol. 19(2), pages 375-404, November.
    2. Paolo Angelis & Roberto Marchis & Mario Marino & Antonio Luciano Martire & Immacolata Oliva, 2021. "Betting on bitcoin: a profitable trading between directional and shielding strategies," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 44(2), pages 883-903, December.
    3. Bianchi, Sergio & Pianese, Augusto, 2018. "Time-varying Hurst–Hölder exponents and the dynamics of (in)efficiency in stock markets," Chaos, Solitons & Fractals, Elsevier, vol. 109(C), pages 64-75.
    4. Sergio Bianchi & Augusto Pianese & Massimiliano Frezza, 2020. "A distribution‐based method to gauge market liquidity through scale invariance between investment horizons," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 36(5), pages 809-824, September.
    5. Ayache, Antoine & Bouly, Florent, 2022. "Moving average Multifractional Processes with Random Exponent: Lower bounds for local oscillations," Stochastic Processes and their Applications, Elsevier, vol. 146(C), pages 143-163.
    6. Marinella Cadoni & Roberta Melis & Alessandro Trudda, 2015. "Financial Crisis: A New Measure for Risk of Pension Fund Portfolios," PLOS ONE, Public Library of Science, vol. 10(6), pages 1-12, June.
    7. Noemi Nava & Tiziana Di Matteo & Tomaso Aste, 2015. "Time-dependent scaling patterns in high frequency financial data," Papers 1508.07428, arXiv.org, revised Dec 2015.
    8. Massimiliano Frezza & Sergio Bianchi & Augusto Pianese, 2022. "Forecasting Value-at-Risk in turbulent stock markets via the local regularity of the price process," Computational Management Science, Springer, vol. 19(1), pages 99-132, January.

    More about this item

    Keywords

    Multifractional processes; efficient markets; behavioral finance; stylized facts;
    All these keywords.

    JEL classification:

    • C00 - Mathematical and Quantitative Methods - - General - - - General
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics

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