CBOE Volatility Index

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CBOE DJIA Volatility Index

CBOE Russell 2000 Volatility Index

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CBOE Skew 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	81
αARCH	0.0277	0.47
βGARCH	0.7932	19.68***
γleverage	0.2081	4.52***
λ₁tau intercept	7.2350	0.47
λ₂forecast adj.	0.2068	0.35
λ₃tau persistence	0.0000	0.00

Parameter	Value	t-statistic
m window Rolling window length	81
α ARCH Response to squared shocks	0.0277	0.47
β GARCH Volatility persistence	0.7932	19.68***
γ leverage Additional response to negative shocks	0.2081	4.52***
λ₁ tau intercept Baseline long-term coefficient	7.2350	0.47
λ₂ forecast adj. Forecast performance sensitivity	0.2068	0.35
λ₃ tau persistence Long-term factor persistence	0.0000	0.00

V-Lab

ProShares UltraPro S&P 500 MF2-GARCH Volatility Analysis

Date Range:

News Impact Curve

Volatility Forecast

Parameter Estimates

Other ProShares UltraPro S&P 500 Analyses