  We compute the value of a variance swap when the underlying is modeled as a
Markov process time changed by a L\'{e}vy subordinator. In this framework, the
underlying may exhibit jumps with a state-dependent L\'{e}vy measure, local
stochastic volatility and have a local stochastic default intensity. Moreover,
the L\'{e}vy subordinator that drives the underlying can be obtained directly
by observing European call/put prices. To illustrate our general framework, we
provide an explicit formula for the value of a variance swap when the
underlying is modeled as (i) a L\'evy subordinated geometric Brownian motion
with default and (ii) a L\'evy subordinated Jump-to-default CEV process (see
\citet{carr-linetsky-1}). {In the latter example, we extend} the results of
\cite{mendoza-carr-linetsky-1}, by allowing for joint valuation of credit and
equity derivatives as well as variance swaps.
