Pricing variance and volatility swaps with stochastic volatility, stochastic interest rate and regime switching

In this paper, we propose a two-factor Heston-CIR hybrid model for the pricing of variance and volatility swaps, by introducing the second regime switching factor into the Heston-CIR hybrid model. While this model is closer to reality, taking advantages of the Heston stochastic volatility, CIR stochastic interest rate and regime switching, it has a more complicated structure and thus leads to extra difficulty in finding analytical solutions. Albeit difficult, we have still managed to present analytical pricing formulae for variance and volatility swaps, based on the derived forward characteristic function in a series form. The series solutions are accompanied by a radius of convergence to ensure its safe application, and their fast convergence demonstrated through numerical experiments facilitates the implementation in practice.