Before revision: A decoupled time-changed (DTC) L\'evy  process is a generalized time-changed L\'evy process whose continuous and discontinuous parts are allowed to follow separate random time scalings . Disentangling the stochastic time change in two components not only provides a powerful unitary framework for the models already present in the literature, but in principle opens up new possibilities for the choice of an asset's log-price dynamics. Following this new idea, we devise a general martingale structure for the price process, and obtain an inverse-Fourier pricing equation for claims paying at maturity a function of the asset value and its realized volatility.
After revision: A decoupled time-changed (DTC) L\'evy process is a generalized time-changed L\'evy process whose continuous and discontinuous parts are allowed to follow separate random time scalings ; we devise the martingale structure for the price process, and obtain an inverse-Fourier pricing equation for claims paying at maturity a function of the asset value and its realized volatility.