Submission: simu.ai

[sitmo]

Submission: simu.ai

This submission presents a regime-switching variance model that reproduces the q-variance relationship using only 2 parameters (σ₀ = 0.25, μ = 0.02).

Model Overview

The model implements a piecewise-constant variance process where:

• Variance regimes switch with Gamma-distributed precision: V_j = 1/τ_j where τ_j ~ Gamma(3/2, rate=σ₀²)
• Log-price increments follow: ΔL_t ~ N(μ·dt, V_j·dt) within each regime
• Regime lengths follow a geometric distribution

The model successfully produces the q-variance relationship: σ²(z) = σ₀² + (z - z₀)²/2

Key Features

• ✅ 2-parameter model (well under the 3-parameter limit)
• ✅ Time-invariant distribution across different period lengths T
• ✅ Long simulation (5M days) for robust statistics
• ✅ Achieves high R² fit to q-variance curve

Files Included

• dataset.parquet - Model output with required columns (ticker, date, T, z, sigma)
• README.md - Detailed model description and implementation details
• method_description.pdf - Extended technical documentation
• model_simulation.py - Core simulation implementation
• generate_submission.py - Script to regenerate the submission
• Figure_1.png - Q-variance scatter plot and fit
• Figure_5.png - Time-invariance demonstration

Implementation

The model can be regenerated by running generate_submission.py, which simulates 5 million trading days and processes the output through the challenge's data loader.

For detailed technical information, please see README.md and method_description.pdf in the submission folder.