The real risk is not in the center — it lives in the tails. Black–Scholes lies because reality jumps. Markets break from events, not from noise. Why this matters in practice ❌ Stop-losses do not protect against jumps ❌ Gaussian VaR is an illusion ❌ “Normal” volatility ignores crises ✅ Options and convexity make sense ✅ Tail-risk hedging exists for a reason ✅ Jump-based models are closer to reality
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