Author: Paul Symonds
A quantized CIR precision process that resolves the alpha = 3/2 infinite-variance instability identified in the competition summary.
The precision Z = 1/V evolves via exact CIR transitions on a discrete lattice. At each daily step, the continuous CIR transition (non-central chi-squared) is computed and quantized to the nearest lattice point. Variance is then V = sigma_0^2 / Z, capped at V_max.
Why it works: The competition proved that any continuous-time model satisfying q-variance requires alpha = 3/2, which makes Var(V) infinite. Quantizing precision onto a discrete lattice makes Var(V) finite while preserving the alpha = 3/2 dynamics. The discretization is not a numerical convenience -- it is essential for convergence.
| Parameter | Value | Role |
|---|---|---|
| sigma_0 | 0.2691 | Base volatility (annualized) |
| kappa | 1.55 | Mean-reversion speed |
| rho | 0.41 | Leverage correlation |
Fixed by theory:
- alpha = 3/2 (from q-variance: k(3/2) = 1/2 gives the z^2/2 coefficient)
- N_max = 200 (structural; insensitive above ~100)
- R^2 = 0.998 (seed 42, 5M days) against the target parabola
- 8/8 seeds pass R^2 >= 0.995 at 5M days (mean 0.997, min 0.996)
- Convergent: R^2 = 0.94 (100K) -> 0.98 (500K) -> 0.997 (1M) -> 0.998 (5M)
- Time-invariant: consistent across all horizons T = 5 to 130
- 500-segment test: all 500 segments processable
Precision lattice:
Z_n = (n + 0.5) * dZ, n = 0, 1, ..., N_max
V_n = min(sigma_0^2 / Z_n, V_max)
CIR dynamics (quantized):
dZ = kappa * (alpha - Z) * dt + sqrt(2 * kappa * Z) * dW
Returns with leverage:
r_t = sqrt(V_t / 252) * (rho * eps_Z + sqrt(1 - rho^2) * eps_perp)
# Generate full submission (5M days, ~10s simulation + ~30s windowing)
python generate_submission.py
# Quick test (500K days)
python simulate.py --days 500000 --seed 42Requirements: Python 3.10+, numpy, pandas, scipy (for scoring only)
| File | Description |
|---|---|
model.py |
Standalone QuantumPrecisionProcess class |
simulate.py |
CLI simulation driver |
generate_submission.py |
End-to-end pipeline (simulate + window + score) |
dataset.parquet |
5M-day windowed dataset (3.85M windows) |
prices_100k.csv |
Sample 100K daily prices |
quantized_precision_paper.md |
Full technical paper |
Paul Symonds