==========================================================================
USRISK  simulate_copula_hawkes  —  copula-Hawkes Monte-Carlo
==========================================================================
interpreter : /opt/homebrew/opt/python@3.14/bin/python3.14
numpy       : 2.4.2

n_nodes  = 3  K(factors) = 2  df = 5
decay    = 0.5  n_steps = 200  dt = 1.0
n_trials = 2000  seed = 12345
A (excitation) = (ones-eye)*0.04:
[[0.   0.04 0.04]
 [0.04 0.   0.04]
 [0.04 0.04 0.  ]]
base_rates (base_intensity per node) = [0.005, 0.027500000000000004, 0.05]
bias = log(base_rates)               = [-5.298317366548036, -3.5935692743096115, -2.995732273553991]
corr = default eye(2);  loadings = default zeros

branching_ratio = spectral_radius(A)/decay = 0.080000/0.5 = 0.160000 (subcritical)

RESULTS
--------------------------------------------------------------------------
branching_ratio          = 0.1600000000
per_node_mean            = [2.8765, 6.8485, 10.8885]
per_node_sd              = [1.8485010760380998, 2.7843175038024808, 3.3015932531134777]
agg_mean                 = 20.6135000000
agg_sd                   = 5.7903265617
agg_VaR99                = 35.0000000000
agg_TVaR99               = 38.8000000000
--------------------------------------------------------------------------
REPRODUCIBILITY CHECK (same seed re-run)
  bitwise-identical on ['per_node_mean', 'per_node_sd', 'agg_mean', 'agg_sd', 'agg_var99', 'agg_tvar99'] : True
  run1 agg_mean = 20.6135
  run2 agg_mean = 20.6135
  run1 agg_var99 = 35.0
  run2 agg_var99 = 35.0
==========================================================================