Simulating Multifractal Asset Returns with Cascades and Fractional Brownian Motion
Summary
The article presents an MQL5 simulation engine for generating synthetic price paths under the Multifractal Model of Asset Returns. It combines three stages: a multiplicative cascade generates uneven trading time, fractional Brownian motion supplies a Gaussian process with long memory, and time deformation composes them into a return process. Model inputs include a Hurst exponent, fitted distribution parameters, sample volatility, and cascade settings; intermediate arrays are retained for inspection.
The cascade draws random multipliers from a selected fitted distribution, creating intervals with differing activity. Fractional Brownian motion is generated with Cholesky decomposition for smaller paths and the Davies–Harte FFT method for larger ones, with fallback to the alternative method if generation fails. The article says validation checks cover cascade invariants, FBM properties, and consistency across runs, but the supplied excerpt does not give their detailed results. It describes a binary cascade implementation and notes that path resolution grows with cascade depth. The engine generates model-based paths; the text does not establish that simulated behavior predicts future market returns or captures all market features.
Key ideas
- The simulation composes a multiplicative cascade’s trading time with fractional Brownian motion to create multifractal paths.
- Cascade multipliers produce a non-uniform measure intended to represent periods of concentrated and sparse activity.
- Cholesky decomposition is used for smaller FBM paths, while Davies–Harte uses FFT methods for larger paths.
- The engine retains intermediate outputs so users can inspect the cascade, trading time, FBM, and final process.
- The supplied material describes validation checks but does not report detailed results or establish predictive value.
Tags
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.