How volatility evolves over time

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{name} Model Equation

How returns affect tomorrow's volatility

How returns affect tomorrow's illiquidity

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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	26
αARCH	0.0446	8.36***
βGARCH	0.8817	76.17***
γleverage	0.1273	11.89***
λ₁tau intercept	10.0000	1.53
λ₂forecast adj.	0.4134	5.64***
λ₃tau persistence	0.5655	7.18***

Parameter	Value	t-statistic
m window Rolling window length	26
α ARCH Response to squared shocks	0.0446	8.36***
β GARCH Volatility persistence	0.8817	76.17***
γ leverage Additional response to negative shocks	0.1273	11.89***
λ₁ tau intercept Baseline long-term coefficient	10.0000	1.53
λ₂ forecast adj. Forecast performance sensitivity	0.4134	5.64***
λ₃ tau persistence Long-term factor persistence	0.5655	7.18***

V-Lab

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