How volatility evolves over time

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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	0.0452	8.12***
βGARCH	0.8776	68.12***
γleverage	0.1283	10.55***
λ₁tau intercept	10.0000	1.96**
λ₂forecast adj.	0.4080	5.68***
λ₃tau persistence	0.5667	7.36***

Parameter	Value	t-statistic
m window Rolling window length	26
α ARCH Response to squared shocks	0.0452	8.12***
β GARCH Volatility persistence	0.8776	68.12***
γ leverage Additional response to negative shocks	0.1283	10.55***
λ₁ tau intercept Baseline long-term coefficient	10.0000	1.96**
λ₂ forecast adj. Forecast performance sensitivity	0.4080	5.68***
λ₃ tau persistence Long-term factor persistence	0.5667	7.36***

V-Lab

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