Fin-Tech Division / The Problem

Discrete-time models fail
at the moment risk management
matters most.

Inside the Stokhos Labs Fin-Tech division, we apply the studio's AI engineering depth to one narrow problem: institutional risk models that underperform in non-stationary regimes. In moments of financial panic, that structural gap becomes catastrophic.

Fin-Tech Division ARX-GARCH ATSMs Discrete-Time Models
Core Failure Modes

Three structural flaws
embedded in every discrete model.

Δt
Fixed Time Steps

ARX-GARCH updates once per day. During a liquidity crisis, conditions shift in minutes, leaving stale data at exactly the wrong moment.

σ²
Static Volatility Structure

GARCH variance is a backward-looking average of past squared errors. Under fat-tailed, regime-switching distributions (standard in crises), the Gaussian assumption produces systematically miscalibrated uncertainty estimates.

∫
No Continuous Adaptation

When a shock arrives, discrete models require recalibration that takes hours or days. By then, positions have moved. A model that updates after the fact is a postmortem tool, not a risk tool.

Mathematical Detail

The assumption that breaks
under market stress.

Discrete-time GARCH

yt = μ + εt
εt = σt zt,  zt ~ N(0,1)
σt2 = ω + αεt−12 + βσt−12

Updates once per period. Gaussian noise hardcoded. Variance is a backward-looking average with no mechanism to incorporate intra-period shocks.

Neural SDE (Stokhos)

dY(t) = fθ(Y(t), t) dt
       + gφ(Y(t), t) dW(t)

Evolves continuously. Diffusion gφ is conditioned on the current state, so uncertainty widens automatically in stressed regimes. No Gaussian constraint.

The Core Problem: Adaptive Latency

Discrete-time models suffer from adaptive latency: the structural delay between when a regime shift occurs and when the model detects it. GARCH variance requires a sequence of large shocks to recalibrate; by the time it registers the new regime, the crisis has already peaked. This isn't a calibration problem. It's a mathematical architecture problem.

Case Study / March 2020 Financial Panic

Beginning March 9, 2020, U.S. Treasury yields dislocated sharply; the 10-year moved more than 50 basis points in a week, bid-ask spreads blew out, and the Fed intervened with emergency purchases. ARX-GARCH, trained on the preceding calm, extrapolated linear trends into a nonlinear regime collapse. Its confidence interval expanded symmetrically but offered no directional signal.

Trained on all available FRED data up to the onset of the panic, the Stokhos Neural SDE cut mean squared forecast error by 64.3% (MSE 0.692 vs. 1.943), with zero retraining.
From the Research
Why GARCH Systematically Misprices Tail Risk in the Belly of the Curve
Read the full analysis →
The Gap

What institutional risk teams
need but don't have.

Current toolkit
  • Daily-recalibrated GARCH with stale intra-day parameters
  • Gaussian VaR that underestimates tail risk in crises
  • Rigid linear factor structure in term structure models
  • Post-hoc stress tests that describe past crises, not future ones
Stokhos platform
  • Continuous-time model that updates as new data arrives
  • State-dependent uncertainty: crisis regimes widen automatically
  • Neural drift + diffusion with no distributional assumptions
  • 64.3% MSE reduction on the hardest out-of-sample stress test available

See the solution.

Drift networks, diffusion networks, Euler-Maruyama integration, and the results behind the Fin-Tech division.

The Approach Risk Dashboard Fin-Tech Overview