A Universal Fractal Framework for Trading Probabilities and Price Corridors

Summary

The article develops a recursive probability framework intended to represent price movement within symmetric, asymmetric, and one-sided corridors. It defines corridor width and midpoint, tracks the current distance from the start of a path, and accumulates step counts and path probabilities. Up and down moves are modeled with probabilities p and 1−p, with binomial combinations used to account for possible sequences before a boundary is reached.

The proposed framework can be adapted to estimate the chance of crossing either boundary, the expected number of steps before a crossing, and quantities such as position lifetime. The author also suggests applications to trading simulations, deposit constraints, and options analysis. These are mathematical and computational proposals rather than demonstrated trading results: the article acknowledges that practical applications remain limited and that deep recursion can demand substantial computation. It presents groundwork for further derivation, with subsequent work expected to simplify the formulas and extend them to backtests and signals.

Key ideas

• The framework treats symmetric, asymmetric, and one-sided price corridors as cases of a general fractal process.
• It tracks distance, accumulated steps, and path probability recursively as the process approaches corridor boundaries.
• Up and down steps are weighted by their respective probabilities, allowing the framework to handle unequal move likelihoods.
• Separate calculations can estimate boundary-crossing probabilities and expected steps to reach each boundary.
• The proposed uses are exploratory, and deep recursive calculations may be computationally expensive.

Tags

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