CBOE Volatility Index

How volatility evolves over time

How illiquidity evolves over time

{name} Model Equation

How returns affect tomorrow's volatility

How returns affect tomorrow's illiquidity

Spline Coefficients

Value at Risk (VaR) estimates the maximum loss at a given confidence level. Expected Shortfall (ES) estimates the average loss beyond VaR.

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Param	Value	t-stat
mwindow	21
αARCH	0.3652	3.81***
βGARCH	0.0000	0.00
γleverage	-0.3491	-3.75***
λ₁tau intercept	0.8870	1.07
λ₂forecast adj.	0.0337	1.46
λ₃tau persistence	0.8000	5.13***

Parameter	Value	t-statistic
m window Rolling window length	21
α ARCH Response to squared shocks	0.3652	3.81***
β GARCH Volatility persistence	0.0000	0.00
γ leverage Additional response to negative shocks	-0.3491	-3.75***
λ₁ tau intercept Baseline long-term coefficient	0.8870	1.07
λ₂ forecast adj. Forecast performance sensitivity	0.0337	1.46
λ₃ tau persistence Long-term factor persistence	0.8000	5.13***

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