The handful of smaller exchanges that support Bitcoin Cash gave everyone who had Bitcoins on their exchanges at the time of the fork an equal balance in Bitcoin Cash, and it's that relatively small amount of on-exchange BCH that people have been trading. (I think one exchange allowed trading before the fork even happened, and just required people to have both BCH and BTC in order to make withdrawals before the fork.) Actual on-chain Bitcoin Cash cannot be sold right now as it can't be deposited in any of the exchanges, and buying it is iffy too due to some of them not allowing withdrawals either. The price of Bittrex BCH has also generally been about 40-50% higher than BCH on the other exchanges for some reason.

At the moment, there are relatively few exchanges where you can trade BCH, and the only BCH on those exchanges is that which was distributed by the exchange itself during the split - as there is no way to move BCH for now.

On the other way, people who want to buy BCH can move their money to those few exchanges, and inflate the bubble, hoping in the greater fool. Ergo, the $700 prices.

In theory, it could be that currently the demand is way higher than the supply, if everyone were able to sell their BCC then the price could crash (assuming everyone would want to sell them as soon as they are able)

Demand to trade them, but it could all come crashing down like an overpriced IPO.