Analytical pricing formulae for variance and volatility swaps with a new stochastic volatility and interest rate model

Abstract

We introduce an additional factor in the Heston-CIR model to form a new hybrid model in this paper. This new model features a more general correlation structure with the interest rate being correlated with the underlying asset, while still preserving the analytical tractability. We derive a series solution to the forward characteristic function when solving a time-dependent Riccati equation, after the measure transform is performed, so that variance and volatility swap prices can be finally written in an analytical form. The theoretical results are also accompanied with some numerical results demonstrating its potential of complementing the usage of the currently adopted non-correlated Heston-CIR model.