  In this paper we propose a general derivative pricing framework which employs
decoupled time-changed (DTC) L\'evy processes to model the underlying asset of
contingent claims. A DTC L\'evy process is a generalized time-changed L\'evy
process whose continuous and pure jump parts are allowed to follow separate
random time scalings; we devise the martingale structure for 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 to more
sophisticated derivatives that pay-off on the joint performance of these two
financial variables, like the target volatility option (TVO). We solve the
pricing problem through a Fourier-inversion method; numerical computations
validating our technique are provided.

Pricing of Securities