  We suggest three superpositions of COGARCH (supCOGARCH) volatility processes
driven by L\'evy processes or L\'evy bases. We investigate second-order
properties, jump behaviour, and prove that they exhibit Pareto-like tails.
Corresponding price processes are defined and studied. We find that the
supCOGARCH models allow for more flexible autocovariance structures than the
COGARCH. Moreover, other than most financial volatility models, the supCOGARCH
processes do not exhibit a deterministic relationship between price and
volatility jumps. Furthermore, in one supCOGARCH model not all volatility jumps
entail a price jump, while in another supCOGARCH model not all price jumps
necessarily lead to volatility jumps.
