Monte Carlo Risk Modeling, Portfolio Optimization & Empirical Envelopes
Actual trading session closes and daily log return fluctuations
Empirical resampling, Black Swan shocks and discrete random-walk paths
Probability of touching the target price before expiry (American) and finishing above it at expiry (European)
Sample window, forecast horizon, number of simulation paths and advanced quantitative filters
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.
Simulates the first-order autocorrelation and clustering persistence of observed returns.
Test of model calibration, Binomial acceptance ranges and the realized 50th percentile using a data hold-out method
| Target Risk Level | Target Ratio | Actual Crossings | Acceptance Range [L - U] | Calibration Status |
|---|
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 |
|---|
Drift deviation (+$0.00), volatility multiplier (1.00x) and validated forecast horizon (100 Days) are applied to the Monte Carlo model automatically after validation.
Return scatter plot, PC0 (Market mode) and PC1 (Minimum variance axis)
Factor exposures (SPY, QQQ, VGT, VUG, VTV, IWM), t-statistics and rolling beta stability
| Factor / Explanatory | Beta (β) Coefficient | Standard Error (SE) | t-Statistic | p-Value | Significance |
|---|
Covariance-matrix-based minimum volatility, maximum Sharpe and 95% bull target solutions
| Symbol | Last Price | Current Shares | Suggested Weight (%) | Suggested Shares | Target Value ($) |
|---|
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 |
|---|
Value at Risk (VaR), Conditional VaR (Expected Shortfall) and extreme tail analysis
Edit the stocks and ETFs in your portfolio, share counts and cash amount.
| Symbol | Shares | Last Price ($) | Total Amount ($) | Action |
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