Analytically pricing variance and volatility swaps with stochastic volatility, stochastic equilibrium level and regime switching

Abstract

This paper proposes a new model with a two-factor stochastic equilibrium volatility level that can be used to price variance and volatility swaps with nonlinear payoff. The adopted model uses the CIR process as the volatility process with the constant equilibrium level replaced with a stochastic one, and at the same time incorporates the regime switching mechanics in order to better describe the underlying price. To better understand how the introduced regime switching impacts both swap prices, we also conduct numerical experiments to compare our results with those obtained without regime switching.