Before revision:  To illustrate our general framework, we provide an explicit formula for the value of a variance swap when the diffusion 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 carr-linetsky-1).
After revision:  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 carr-linetsky-1).