21  Time Makes Tails Worse

Introduces volatility clustering and autocorrelation with a minimal from-scratch GARCH-style toy model, showing that “today’s variance depends on yesterday’s shock” is enough to produce fat-tailed behavior even from an underlying process that isn’t fat-tailed step-by-step.

def toy_garch_step(prev_variance, prev_shock, omega=0.1, alpha=0.3, beta=0.6):
    return omega + alpha * prev_shock**2 + beta * prev_variance