QUANTITATIVE ANALYSIS ENGINE

MONTE CARLO STOCK SIMULATOR

Probabilistic price forecasting using Geometric Brownian Motion. 90% validated accuracy across 30+ historical backtests.

▶ LAUNCH SIMULATOR ◈ VIEW METHODOLOGY
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ACCURACY
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SIMULATIONS/SEC
0.67
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STAT. SIGNIFICANCE
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01 // CAPABILITIES

SYSTEM FEATURES

GBM SIMULATION

Geometric Brownian Motion with drift and diffusion. Vectorized computation delivers 10,000 simulations in under a second.

CORE ENGINE

FAT-TAIL MODELING

Student-t distribution captures extreme market events — crashes and rallies that Normal distribution underestimates.

DISTRIBUTIONS

RISK METRICS

Value at Risk (95%, 99%), Sharpe Ratio (ex-ante & ex-post), probability of profit/loss, and confidence intervals.

ANALYTICS

MODEL COMPARISON

Side-by-side Normal vs Student-t simulation. Compare confidence intervals, VaR, and tail behavior in real time.

COMPARISON

BACKTESTING

Automated historical validation with 30+ test windows. Christoffersen's conditional coverage test for statistical rigor.

VALIDATION

REGIME ANALYSIS

Volatility regime classification (Low/Medium/High). Model performance breakdown by market conditions.

INTELLIGENCE
02 // SIMULATION ENGINE

MONTE CARLO TERMINAL

CONFIGURATION
$
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Enter ticker & press FETCH
100 10,000
-20%⟳ AUTO‑CALIBRATED50%
5%⟳ AUTO‑CALIBRATED80%

CONFIGURE & RUN

Set your parameters and hit RUN SIMULATION to generate Monte Carlo price paths

↑↓ Adjust parameters ENTER Run simulation
03 // BACKTESTING ENGINE

MODEL VALIDATION

BACKTEST CONFIGURATION
$
04 // MATHEMATICAL FRAMEWORK

METHODOLOGY

CORE MODEL

Geometric Brownian Motion

S(t+1) = S(t) × exp((μ - ½σ²)Δt + σ√Δt × ε)
μ Mean of daily log returns (estimated from historical data)
σ Standard deviation of log returns (realized volatility)
ε Random shock ~ N(0,1) or Student-t(df)
Δt Time step = 1 trading day
STUDENT-T

Fat-Tail Modeling

Real markets exhibit fatter tails than the Normal distribution predicts. The Student-t distribution with low degrees of freedom captures extreme events more accurately.

KEY INSIGHT Lower df → fatter tails → wider confidence intervals → more conservative risk estimates
RISK METRICS

Quantitative Analysis

VaR (95%) Maximum expected loss at 95% confidence
VaR (99%) Extreme tail risk measure
Sharpe Ratio Risk-adjusted return (excess return / volatility)
90% CI 5th–95th percentile price range
ASSUMPTIONS

Model Limitations

⚠ Constant volatility — real σ is time-varying
⚠ No jumps or mean reversion
⚠ No fundamental factors (earnings, macro)
⚠ Historical parameters may not persist
05 // VALIDATION RESULTS

PERFORMANCE

90 %

BACKTEST ACCURACY

90% of actual prices fell within model's 90% confidence interval across 30+ validation windows

0.67 p

P-VALUE

Binomial test confirms coverage is statistically consistent with expected 90% — model is well-calibrated

<1 s

EXECUTION TIME

1,000 fully vectorized simulations complete in under 1 second — optimized for real-time analysis

FAILURE MODE ANALYSIS
CONDITION IMPACT SEVERITY
High Volatility Regimes Hit rate drops ~5-10% MEDIUM
Regime Changes (Bull→Bear) Model lags behind transitions HIGH
Black Swan Events Even Student-t underestimates extremes CRITICAL
Long Horizons (>3 months) Intervals become very wide (50%+) MEDIUM