how does the cboe volatility index (the VIX) work as well as the options on the VIX?

Answer 1

The Vix uses the calls and puts on the Chicago Board Option Exchange to calculate an index. Option pricing (Black Scholes) uses inputs, to which all of the variables are known with certainty except one... implied volatility.

This implied volatility is, out of a lack of a better analogy, the "discount rate" on the options. Basically, it's pricing in how much volatility is implied by the market - more volatility is good because of the greater chance of an option being in the money before the end of expiration.

The Vix measures volatility implications, putting into an index. Below 20 means the market is pretty relaxe and above 30 means that the market is spooked. Usually, the VIX is used as a contrarian indicator. When the market is spooked, usually things aren't all that bad and you can start going long. When a market is complacent (like it is now), that's when you got to start worrying because the market is factoring in some pretty smooth sailing without Mr. Murphy and his law.