The primary reason that we normally see the VIX dip down on Fridays and then pick back up on Mondays is simply because of time decay.
Option prices late Friday (providing there is not excess volatility on this day that would make traders nervous over the weekend) begin to reflect the fact that there will be two days of time decay over the weekend.
For example, given the same level of volatility, an option price that is trading at $1 on Friday would only be worth $.95 on Monday. So late Friday that option will begin to trade down to around $.97 to reflect this.
This has the effect of driving the implied volatility of that option down on Friday and consequently the VIX. On Monday with the option price now at $.95, the implied volatility and the VIX is back up to the same level as it was the previous Thursday.
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