  In equity and foreign exchange markets the risk-neutral dynamics of the
underlying asset are commonly represented by stochastic volatility models with
jumps. In this paper we consider a dense subclass of such models and develop
analytically tractable formulae for the prices of a range of first-generation
exotic derivatives. We provide closed form formulae for the Fourier transforms
of vanilla and forward starting option prices as well as a formula for the
slope of the implied volatility smile for large strikes. A simple explicit
approximation formula for the variance swap price is given. The prices of
volatility swaps and other volatility derivatives are given as a
one-dimensional integral of an explicit function. Analytically tractable
formulae for the Laplace transform (in maturity) of the double-no-touch options
and the Fourier-Laplace transform (in strike and maturity) of the double
knock-out call and put options are obtained. The proof of the latter formulae
is based on extended matrix Wiener-Hopf factorisation results. We also provide
convergence results.
