Abstract
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.
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