MCarloRisk Quantitative Suite

Monte Carlo Risk Modeling, Portfolio Optimization & Empirical Envelopes

Real Market Data Ready
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Last Close Price
$0.00
Daily Return: +0.00%
Annualized Return (μ)
0.00%
Based on 252 trading days
Annual Volatility (σ)
0.00%
Daily σ × √252
Sharpe Ratio (RFR=4%)
0.00
Risk-free adjusted
Skewness
0.00
Asymmetry coefficient
Kurtosis
0.00
Excess tail / Fat-tail

Historical Price and Daily Return Distribution

Actual trading session closes and daily log return fluctuations

Monte Carlo Probability Envelopes and Future Projection

Empirical resampling, Black Swan shocks and discrete random-walk paths

Upper Slider: Probability Percentile 50% (Median)
Price at Horizon: $0.00
Lower Slider: Timeline (Trading Day) Day 21
5%-50%-95% Range on Day:  |  $0.00-$0.00-$0.00
Chart Start: Days of History Start From Now
The chart starts 0 days before now — past prices are shown
99% / 95% / 90% (Upper Envelope) 50% Median Forecast Current Price (Zero-Slope Ref) 10% / 5% Lower Risk 1% Extreme Risk (Red Limit) Selected Percentile
Strike Price & Option Probabilities

Probability of touching the target price before expiry (American) and finishing above it at expiry (European)

Probability of Touching Before Expiry
—
American-style P(Max ≥ Strike)
Finishing on Target Side at Expiry
—
European-style expiry probability
Model Call Premium (Monte Carlo)
—
Black-Scholes: —
Model Put Premium (Monte Carlo)
—
Black-Scholes: —
Model Parameters and Fine-Tuning (Lookback, Forecast, Filters)

Monte Carlo Model Parameters and Fine-Tuning

Sample window, forecast horizon, number of simulation paths and advanced quantitative filters

504 Days (2 Years)
Number of past trading days the model is trained on (Default: 2 Years / 504 Days)
21 Days (1 Month)
Number of days to simulate forward (can be auto-matched to the ideal validation horizon on the Validate tab)
Number of Monte Carlo random walks (Default: 10,000)
0.50
<0.5: Mean-reverting, 0.5: Random (i.i.d.), >0.5: Trend-following
0.00
Marcos Lopez de Prado memory-preserving stationarization (0=Price, 1=Return)
0.0
0: Equal weights, 1: Linear decay, 2: Quadratic (weights recent history)

Black Swan Shock Generator

Shock Size (%): 7.0%
Shock Frequency (%/day): 1.0%

Volatility Model & Reproducibility

If EWMA (RiskMetrics, λ=0.94) is selected, the simulation starts from current volatility and reacts to shocks (volatility clustering). If a seed is set, the same settings produce the same result.

Serial Sampling

Simulates the first-order autocorrelation and clustering persistence of observed returns.

Comprehensive Backward Validation (Backtest & AcceptRanges)

Test of model calibration, Binomial acceptance ranges and the realized 50th percentile using a data hold-out method

Actual Market Price (Dark Blue Line) 99% / 95% Upper Risk Envelope Model 50% Median (Realized 50th Percentile) 5% Lower Risk (Realized 5%) 1% Extreme Risk Band
Binomial Acceptance Ranges (AcceptRanges) and Diagnostic Report
Target Risk Level Target Ratio Actual Crossings Acceptance Range [L - U] Calibration Status
Mean Residual Error (Δμ)
$0.00
Drift Correction Amount
Residual Deviation (Std Err)
$0.00
Error distribution width
Volatility Scale Multiplier (c_σ)
1.00x
σ_realized / σ_modeled
Overall Calibration Diagnosis
—
Model fit
Rolling-Origin Backtest (Kupiec & Independence Test)

The model is built at many different historical start points using only data up to that day, then simulated forward over the forecast horizon. The realized end-of-horizon price is compared with the forecast percentiles. Start points are spaced one horizon apart, so they do not overlap.

Level Target Ratio Actual (breaches / n) Kupiec p Independence p Result
⚡ Predictor-Corrector Calibration Inactive

Drift deviation (+$0.00), volatility multiplier (1.00x) and validated forecast horizon (100 Days) are applied to the Monte Carlo model automatically after validation.

Manual Correction Parameters (Fine-Tuning)
Linear mean-shift correction
Diffusion scaling multiplier

Principal Component Analysis (PCA) & Hedge Portfolio

Return scatter plot, PC0 (Market mode) and PC1 (Minimum variance axis)

PC0 Explained Variance (Maximum)
0.0%
Systemic Market Risk Direction
PC1 Explained Variance (Minimum)
0.0%
Hedge / Min-Volatility Axis
PC1 Minimum Volatility Weights
w1: 0%, w2: 0%
Normalized eigenvector weight
Two-Asset Correlation (R)
0.00
R² = 0.00

Multi-Factor Alpha & Beta Regression and Stability Tracking

Factor exposures (SPY, QQQ, VGT, VUG, VTV, IWM), t-statistics and rolling beta stability

Factor / Explanatory Beta (β) Coefficient Standard Error (SE) t-Statistic p-Value Significance
Annualized Alpha (α)
0.00%
Excess return over factors
Coefficient of Determination (R²)
0.000
Model explanatory power
Adjusted R² (Adj R²)
0.000
Degrees-of-freedom adjusted
F-Statistic
0.00
Overall model test

Rolling Beta & Alpha Stability (Rolling 126-Day Window)

Markowitz Portfolio Optimization & Efficient Frontier

Covariance-matrix-based minimum volatility, maximum Sharpe and 95% bull target solutions

Optimal Portfolio Allocation and Share Counts

Symbol Last Price Current Shares Suggested Weight (%) Suggested Shares Target Value ($)

3D / 2D Option Pricing and Open Position Grid

Monte Carlo vs Black-Scholes premium comparison across strike prices and expiries

Expiry (Trading Days) Strike Price Distance to Price (%) Monte Carlo Call ($) Black-Scholes Call ($) Monte Carlo Put ($) Black-Scholes Put ($) Touch Probability

Comprehensive Quantitative Risk Report & Portfolio Audit

Value at Risk (VaR), Conditional VaR (Expected Shortfall) and extreme tail analysis

95% Value at Risk (VaR 95%)
$0.00
0.00% capital loss
99% Value at Risk (VaR 99%)
$0.00
0.00% capital loss
95% Conditional VaR (CVaR)
$0.00
Expected Shortfall (Tail Average)
99% Conditional VaR (CVaR)
$0.00
Extreme Crisis Expected Loss
Maximum Historical Drawdown (MDD)
0.00%
Maximum decline from peak
Model Calibration Score
A+ (Excellent)
AcceptRange success rate

Executive Summary and Mathematical Validation