GBM Simulation: DE — started 2026-03-01

Symbol: DE  |  Start: 2026-03-01  |  Run days: 19  |  Sector: Industrials

Regime State

Technical State Detail

Regime Switching (Hamilton)

Current regime: 0 — Inflationary / Expanding / Tightening

Simulation Chart

Price Table

How to Read the Chart

• Thin blue lines: individual GBM Monte Carlo price paths (each represents one possible future).
• Blue shaded band: 10th–90th percentile range across all traces.
• Red dashed: mean (expected) price path.
• Green dashed: median price path.
• Orange dashed: minimum price path across all traces.
• Purple dashed: maximum price path across all traces.
• Black solid: actual closing price (available only for dates with historical data).

The divergence of the band over time reflects model uncertainty. Actual prices falling outside the 10–90th percentile band indicate regimes not well-captured by the model inputs at the simulation start date.

Methodology

Merton Jump-Diffusion with Hamilton regime switching and daily steps (Δt = 1/252):

S_{t+1} = S_t × exp( (μ_{r_t} − σ_{r_t}²/2 − λ·k̄)·Δt + σ_{r_t}·√Δt·Z + N_t·J_t )
  r_t ~ P(r_{t+1}|r_t)   (Hamilton Markov regime; daily transition matrix)
  Z   ~ N(0,1)             (diffusion)
  N_t ~ Poisson(λ·Δt)     (jump count per step)
  J_t ~ N(μ_J, σ_J)       (log jump size)
  k̄   = exp(μ_J + σ_J²/2) − 1 = +0.0152  (expected price jump size)

Regime switching: Hamilton (K=9) — current regime 0 (Inflationary / Expanding / Tightening)
  μ_{r_t} = 0.0772  σ_{r_t} = 0.4003  (current regime values)

μ_i  = r_f  +  β · λ_MRP  +  α_sector  +  α_momentum  +  α_technical
     = 0.0364 + 1.0040×-0.0200 + +0.00813 + +0.03866 + +0.01407
     = 0.0772  (annualized drift)

σ_ε  = (1−0.4)·σ_OLS  +  0.4·σ_ATR
     = 0.6·0.3005  +  0.4·0.4716
     = 0.3689

σ_i  = √( β² · σ_m²  +  σ_ε_blended² )
     = √( 1.0040²·0.1548²  +  0.3689² )
     = 0.4003  (annualized total volatility)

Jump parameters (estimated from 252d return fat tails, threshold = 2.5σ):
  λ        = 6.0239  (~1518.0 jumps/year expected)
  μ_J      = +0.0124  (mean log jump size)
  σ_J      = 0.0743  (jump size std dev)
  k̄        = +0.0152  (drift correction applied)

Parameter Sources

• r_f: Federal Funds Rate (S3 regime/economic/federalFunds.parquet) → fallback 3-mo T-bill → 4%
• β: Asset beta from key_metrics (S3 fundamentals), as of 2026-03-01
• λ_MRP: Base market risk premium (FMP market-risk-premium) adjusted by GDP momentum, HY OAS change, and consumer sentiment
• α_sector: Industrials 60-day cumulative return vs. all-sector mean, scaled to annual contribution
• α_momentum: W5 × (price − MA200) / MA200 (W5 = 0.15)
• α_technical: Computed from prior 10 trading days — RSI(14) level & slope, price-vs-EMA/DEMA/TEMA stack, EMA_DT trend fraction, and 10-day combined signal score (Donchian + TEMA crossover + Keltner + EMA_DT), each scaled and summed → clipped to [−5%, +5%] annual
• σ_m: W6·VIX_norm + W7·σ_realized + W8·ΔNFCI (weights: 0.5/0.4/0.1)
• σ_ε: Blended — 60% OLS residual vol (symbol log-ret ~ VIX log-chg, 252d) + 40% ATR-realized vol (ATR(20)/close × √252)
• Jump parameters: Estimated from prior 252 trading days. Days where |log_ret − mean| > 2.5σ are classified as jumps. λ = annualized jump frequency; μ_J and σ_J from the empirical jump return distribution. Falls back to λ=0.05, μ_J=−0.02, σ_J=0.03 if fewer than 2 jumps detected.
• Regime switching: K=9 regimes from cluster_weekly_central_bank.parquet. Empirical weekly transition matrix built from consecutive cluster_id observations, then scaled to daily (off-diagonal ÷ 5). Per-regime σ_k = σ_i × (VIX_k / VIX_current); per-regime μ_k = μ_i − (HY_OAS_k − HY_OAS_current) × W3_HY. All traces start in the current regime.

Data sourced from Financial Modeling Prep API and FRED (St. Louis Fed), pre-fetched to S3 by update_data.py regime.