Product
Liminal Motion
A synthetic data engine for financial stress testing, built on four mathematical layers. Generate unlimited, mathematically grounded scenario paths with any prescribed distribution.
Move your mouse to change the Julia set parameter c
Architecture
Four mathematical layers
Each layer addresses a distinct requirement. Together they produce synthetic returns with exact statistical properties and full mathematical transparency.
Layer 1: Julia Set Dynamics
Backward iteration on f(z) = z2 + c produces a temporal skeleton. The Brolin-Lyubich invariant measure provides stationarity. The parameter c controls geometry.
Layer 2: Quantile Transport
The Radon-Nikodym bridge h = Fν-1 ∘ Fπ maps Julia marginals to any target distribution. Student-t, empirical, Cauchy — exact marginals, preserved temporal structure.
Layer 3: GARCH(1,1)
Transported innovations drive GARCH volatility dynamics, producing realistic volatility clustering combined with fat tails. Two-stage calibration via quasi-MLE.
Layer 4: Multi-Asset Dependence
Gaussian copula on branch sequences injects cross-asset correlation while preserving all per-asset theorems. Four independent control knobs.
Pre-Calibrated
Seven crisis archetypes
Ready-to-deploy scenarios, each defined by a specific c parameter.
Symmetric Vol Shock
c = 0
Arcsine tails, uniform high volatility.
Two-Regime Crisis
c = -0.5 + 0.5i
Bimodal returns, regime switching.
Fat-Tail Turbulence
c = -0.75
Heavy-tailed symmetric stress.
Gap / Jump Risk
c = 0.3 + 0.5i
Disconnected support, discrete jumps.
Spiralling Drawdown
c = -0.12 + 0.75i
Asymmetric drawdown with bias.
Double-Dip
c = -1.0
Clustered bimodal recession.
Transparency
Honest limitations
We believe transparency is essential for trust in quantitative tools.
Fast mixing, not persistence
After quantile transport, autocorrelation decays exponentially. GARCH adds volatility clustering but does not produce return-level momentum.
Static regime
The parameter c is constant per simulation. For dynamic regimes, couple with a Hidden Markov Model (roadmap Phase 3).
Symmetric GARCH
Standard GARCH treats shocks symmetrically. GJR-GARCH for leverage effects is roadmap Phase 2.