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Monte Carlo Multi-Asset Empirical Engine v3.7

ENGINE ONLINE

Wharton CRSP / Compustat Institutional Return Innovations • Stochastic Risk Matrix

μ
Drift-Corrected GBM
Itô Bias Corrected
Drift-Corrected Compounding

In continuous log-returns, volatility adds an accidental upward drift. Itô's Lemma applies a -½σ² correction so expected prices match mathematical returns.

✓ Prevents artificial upward price inflation
ν
Fat-Tail Shock Model
Student's t Jump Risk
Student's t Jump Shock Model

Real markets experience sudden flash crashes that standard bell curves ignore. Student's t innovations with fitted degrees of freedom (ν) simulate realistic tail shocks and fat-tail kurtosis.

✓ Protects against sudden market crashes
>0
Zero-Floor Guard
Strict Limited Liability ($P>0)
Limited Liability ($P_t > 0)

Stock prices have limited liability and cannot drop below zero. By compounding log-returns exponentially (P_t = P_0 • exp(r)), prices can approach zero in extreme downturns but never turn negative.

✓ Guaranteed positive asset valuation
10K
10,000 GPU Paths
Parallel Stochastic Grid
CUDA GPU Parallel Paths

Simulates 10,000 independent stochastic paths per asset in parallel on GPU cores to calculate exact empirical 99% Value-at-Risk (VaR), 99% CVaR tail loss, and alpha win probabilities.

✓ Institutional quantile precision
30D
30-Day Forecast
Daily Step Trajectory
30-Step Forward Projection

Projects daily price evolution forward 30 discrete trading steps (approximately 1 calendar month of trading) starting from the live spot price (p₀).

✓ 1-Month forward path cone
⚠️ Mandatory Research & Accuracy Disclosure
Academic & Quantitative Research Only

STRICT RESEARCH NOTICE • ASSUMPTION OF INACCURACY: All models, simulations, algorithmic signals, parameter values, factor regressions, and analytical outputs presented across this platform are provided strictly for quantitative and academic research purposes only. All data points, financial metrics, and market values are assumed to be unverified and inaccurate until independently audited and verified against official regulatory filings (SEC XBRL) and primary exchange trade records. Nothing on this website constitutes investment, legal, tax, or financial advice.

NVDA

NVDA

RESONANT
Market Regime State

Classifies overall statistical coherence into 4 states: Resonant (high alpha alignment), Ordered (stable equilibrium), Fracture (elevated tail volatility), or Dormant (low kinetic participation).

STUDENT-T (df=6.04)
Statistical Innovation Engine

Automatically switches between Student's t (heavy-tail shocks with fitted degrees of freedom) and standard Gaussian based on asset kurtosis.

Synced: 2026-08-29 17:35:00 • Wharton Daily Log-Return
Spot (p₀)
$217.97
30-Step Target
$217.54 -0.20%
-$0.43 drift
Expected Price Target

The mathematical average price at step 30 across all 10,000 drift-corrected Monte Carlo paths, accounting for compounding volatility and historical momentum.

99% VaR30d
$2.38
1.09% max shock
99% Value at Risk (30d)

Maximum expected loss at 99% confidence. 99% of simulated 30-day outcomes stay above this downside floor (1-in-100 path stress test) stay above this floor.

✓ Downside risk floor
99% CVaRTail
$2.89
1.33% tail loss
99% Conditional VaR

Average expected loss during the worst 1% catastrophic tail crash tail scenarios beyond VaR.

✓ Extreme tail loss severity
Alpha WinP(+)
35.8%
Positive Win Probability

Percentage of 10,000 simulated futures ending with positive return (P₃₀ > P₀).

✓ Bullish directional odds
Kurtosisdf 6.04
5.94
Heavy Fat-Tail
Tail Fatness & Jump Risk

Kurtosis > 3.0 indicates fat tails. Lower degrees of freedom (df) signal high flash-crash vulnerability.

✓ Outlier shock propensity
Hurst (H)Fractal
0.417
Mean Reverting
Fractal Memory Index (H)
• H > 0.55Trending
• H ≈ 0.50Random Walk
• H < 0.45Mean-Reverting
✓ Price memory regime
Rev Pressuret=3.5
63.8%
Friction Barrier
Reverse Pressure (Rp)

Structural friction index measuring resistance against price continuation. High percentages signal strong order-flow friction and trend exhaustion.

Proprietary Resistance Index

Student's t vs Normal Distribution

Fitted: df = 6.04

Fat Tail Normal
ⓘ Fat-Tail Significance: Student's t innovations simulate realistic market jumps, preventing underestimation of sudden shocks that standard Gaussian models miss.

30-Step GBM Paths & VaR Floor

10,000 CUDA iterations with non-overlapping staggered value tags

Target VaR Spot
✓ Anti-Collision Layout: Right-axis value tags dynamically stagger and use leader lines when Spot and Target prices converge, eliminating all overlapping text smudges.

Verified Market Database 242 Assets (Sovereign 250)

Click any row to focus that asset above

Ticker ⇅ Spot ⇅ Target ⇅ Return% ⇅ 99% VaR ⇅ 99% CVaR ⇅ Alpha% ⇅ Kurt ⇅ df ⇅ Hurst ⇅ Rp ⇅ Regime ⇅