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Asset Price Modeling: From Fractional to Multifractional Processes

In: Future Perspectives in Risk Models and Finance

Author

Listed:
  • Sergio Bianchi

    (University of Cassino)

  • Augusto Pianese

    (New York University)

Abstract

This contribution surveys the main characteristics of two stochastic processes that generalize the fractional Brownian motion: the multifractional Brownian motion and the multifractional processes with random exponent. A special emphasis will be devoted to the meaning and to the applications that they can have in finance. If fractional Brownian motion is by now very well-known and studied as a model of the price dynamics, multifractional processes are yet widely unknown in the field of quantitative finance, mainly because of their nonstationarity. Nonetheless, in spite of their complex structure, such processes deserve consideration for their capability to seize the stylized facts that most of the current models cannot account for. In addition, their functional parameter provides an insightful and parsimonious interpretation of the market mechanism, and is able to unify in a single model two opposite approaches such as the theory of efficient markets and the behavioral finance.

Suggested Citation

  • Sergio Bianchi & Augusto Pianese, 2015. "Asset Price Modeling: From Fractional to Multifractional Processes," International Series in Operations Research & Management Science, in: Alain Bensoussan & Dominique Guegan & Charles S. Tapiero (ed.), Future Perspectives in Risk Models and Finance, edition 127, pages 247-285, Springer.
    • Handle: RePEc:spr:isochp:978-3-319-07524-2_7
    DOI: 10.1007/978-3-319-07524-2_7
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    Cited by:

    1. Axel A. Araneda, 2023. "A multifractional option pricing formula," Papers 2303.16314, arXiv.org, revised Jun 2024.
    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.

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