On Tuesday, you calculated the volatility of Wednesday as 5% using the GARCH model, which information will make the Thursday volatility become even higher?

Question

BlackTom AI · Accepted Answer

To reason through how Thursday’s volatility could become higher in a GARCH framework, we examine how past information affects the conditional variance.
Option 1: 'Return on Tuesday very low' — A low Tuesday return would generally contribute a smaller squared return term and a smaller update to the volatility estimate from that past observation. Therefore, it does not provide the trigger for higher Thursday volatility.
Option 2: 'Return on Wednesday very high' — This is the plausible driver. In a GARCH model, yesterday’s squared return (and the previous volatility) feed into today's (or next period’s) conditional variance. A very high Wednesday return increases the last period’s shock, which raises the estimated volatility for Thursday through the ARCH and GARCH update terms, making Thursday volatility higher.
Option 3: 'Return on Thursday very low' — Thursday’s own return cannot influence Thursday’s volatility in a forward-looking way; volatility is updated based on past information, not the concurrent or future return. A low Thursday return does not explain why Thursday’s volatility would rise.
Option 4: 'None of the above' — Since there is a logically consistent mechanism in Option 2 (a high Wednesday return increasing Thursday’s volatility in GARCH), this blanket negation is incorrect.
In summary, the key concept is that larger past shocks (such as a very high Wednesday return) feed into higher next-period conditional variance, which is the mechanism by which Thursday volatility would become higher. Conversely, low past returns or a distant future observation do not provide the same effect in a standard GARCH updating rule.

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On Tuesday, you calculated the volatility of Wednesday as 5% using the GARCH model, which information will make the Thursday volatility become even higher?

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