Empirical Volatility Model

A normal curve returns a symmetric range because symmetry is the only shape it knows. Real returns are skewed and fat tailed, so the confidence bands here are built from the realized distribution of the asset itself and placed next to the normal ones, where the distance between the two is usually the part worth reading.

• Price ranges drawn from the empirical distribution of realized returns
• Skew and excess kurtosis preserved, so the upside and downside bands are free to differ
• The normal model bands shown alongside, so the size of that assumption becomes measurable