An Unconventional Attempt to Tame Mandelbrot's Grey Swans

TL;DR

This paper introduces a novel physical model for market pricing that considers multiple time scales independently, enabling volatility estimation and price direction forecasting without historical data calibration, aligning with real market properties.

Contribution

It presents a new theoretical approach to market pricing using independent equations for different time scales, avoiding calibration on historical data.

Findings

Model captures fat tails and scaling properties.

Enables forecasting of market price directions.

Consistent with real market behaviors.

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.