Pricing variance swaps in a hybrid model of stochastic volatility and interest rate with regime-switching

TL;DR

This paper develops a semi-closed form pricing formula for discretely-sampled variance swaps within a hybrid stochastic volatility and interest rate model that incorporates regime-switching, extending the Heston model with CIR interest rates.

Contribution

It introduces a novel hybrid model with regime-switching for variance swap pricing and derives a semi-closed form formula for practical implementation.

Findings

Regime-switching significantly affects variance swap prices.

The derived formula is validated through numerical simulations.

Including interest rate dynamics improves pricing accuracy.

Abstract

In this paper, we consider the problem of pricing discretely-sampled variance swaps based on a hybrid model of stochastic volatility and stochastic interest rate with regime-switching. Our modelling framework extends the Heston stochastic volatility model by including the CIR stochastic interest rate and model parameters that switch according to a continuous-time observable Markov chain process. A semi-closed form pricing formula for variance swaps is derived. The pricing formula is assessed through numerical implementations, and the impact of including regime-switching on pricing variance swaps is also discussed.