A series-form solution for pricing variance and volatility swaps with stochastic volatility and stochastic interest rate

In this paper, we present analytical pricing formulae for variance and volatility swaps, when both of the volatility and interest rate are assumed to be stochastic and follow a CIR (Cox-Ingersoll-Ross) process, forming a Heston-CIR hybrid model. The solutions are written in a series form with a theoretical proof of their convergence, ensuring the accuracy of the determined swap prices. The application of the formulae in practice is also demonstrated through the designed numerical experiments.