Modeling Asymmetric Price Corridors with Fractal Nesting

Summary

The article develops a mathematical model for the average number of price steps before a boundary is crossed in symmetric and asymmetric corridors. It begins with a product rule for the two corridor halves, then generalizes the model to directional step probabilities by assigning probability-dependent exponents to each half. The exponents are represented by simple power-function prototypes, whose coefficients are sought by random search against simulated data.

The model is expanded to estimate boundary-crossing probabilities and directional step counts, then assembled into a full mathematical model and compared with simulation results. The article reports that the model and simulation matrices largely agree. It attributes residual differences to imperfect function prototypes and simulation limits, especially at larger corridor sizes. The framework is exploratory: it is derived from fractal-nesting assumptions and simulated random processes, and the excerpt does not establish predictive performance on live market data or provide independent empirical validation.

Key ideas

• The symmetric corridor formula is treated as a special case of a model for asymmetric corridor halves.
• The proposed average step count multiplies each half’s size raised to a probability-dependent exponent.
• The model uses fractal nesting as the key constraint on its functional form.
• Simple power-function prototypes are fitted by random search against simulated observations.
• The full model is checked against simulation, with discrepancies attributed to prototype and simulation limitations.

Tags

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.