You cannot buy the VIX. It is a calculation, not a portfolio, so the only way to trade it directly is through futures that settle to it. Each contract is worth $1,000 per point, so a move from 15 to 18 is $3,000.
Crucially, a VIX future prices expected volatility over the 30 days after its own expiry, not today's VIX. That is why the front future can sit at 17 while spot VIX is 13, and why VIX futures move far less than spot on a panic day. The contract also settles on a Wednesday, thirty days before the following month's SPX option expiry, not on the usual third Friday.
Almost every volatility exchange-traded product is built from these contracts and inherits their roll-yield, which in the usual upward-sloping vix-term-structure is strongly negative.
Example: spot VIX 14.0, front future 15.8, second month 17.0. Holding the front month one month costs the 1.2-point roll, $1,200 per contract, before any change in volatility.
Related: vix-term-structure, vro-settlement, roll-yield, implied-volatility, contango