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An Unconventional Attempt to Tame Mandelbrot's Grey Swans

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  • Denis M. Filatov
  • Maksim A. Vanyarkho

Abstract

We suggest an original physical approach to describe the mechanism of market pricing. The core of our approach is to consider pricing at different time scales separately, using independent equations of motion. Such an approach leads to a pricing model that not only allows estimating the volatility of future market prices, but also permits forecasting the direction of the price move. Alongside with that, it is crucial that our model implies no calibration on historical market data. And last but not least, properties of the model's solution are consistent with those of real markets: it has fat tails, possesses scaling and evinces nonlinear market memory. As our model has been derived with the tip of the pen, it may be not a yet another confirmation of the known empirical facts, but a theoretical justification thereto. Tests on real financial instruments prove the competence of our approach.

Suggested Citation

  • Denis M. Filatov & Maksim A. Vanyarkho, 2014. "An Unconventional Attempt to Tame Mandelbrot's Grey Swans," Papers 1406.5718, arXiv.org.
    • Handle: RePEc:arx:papers:1406.5718
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    References listed on IDEAS

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    1. Contreras, Mauricio & Pellicer, Rely & Villena, Marcelo & Ruiz, Aaron, 2010. "A quantum model of option pricing: When Black–Scholes meets Schrödinger and its semi-classical limit," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(23), pages 5447-5459.
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    3. J. B. Glattfelder & A. Dupuis & R. B. Olsen, 2010. "Patterns in high-frequency FX data: discovery of 12 empirical scaling laws," Quantitative Finance, Taylor & Francis Journals, vol. 11(4), pages 599-614.
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