Before revision:  Thus with a single formula we are able to capture prices for derivatives depending on either an asset or its volatility , but also joint payoffs are allowed , like the target volatility option (TVO) , which shall be discussed.
After revision:  Thus with a DTC L\'evy-driven asset and revisit many popular models which fall under this framework. Postulating different time changes for the underlying L\'evy decomposition allows to introduce asset price models consistent with the assumption of a correlated pair of continuous and jump market activities; we study one illustrative DTC model having this property by assuming that the instantaneous activity rates follow the the so-called Wishart process. The theory developed is applied to the problem of pricing claims depending not only on the price or the volatility of an underlying asset , but also joint payoffs are allowed , like the target volatility option (TVO) , which shall be discussed.