Pricing of Variance Swaps under a Credit-Equity Modeling Framework

Abstract

We compute the value of a variance swap when the underlying is modeled as a Markov process time changed by a Levy subordinator. In this framework, the underlying may exhibit jumps with a state-dependent Levy measure, local stochastic volatility and have a local stochastic default intensity. Moreover, the Levy 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 diffusion is modeled as (i) a Levy subordinated geometric Brownian motion with default and (ii) a Levy subordinated Jump-to-default CEV process. Our results extend the results of, by allowing for joint valuation of credit and equity derivatives as well as variance swaps.