Pricing variance swaps with stochastic volatility and stochastic interest rate under full correlation structure

TL;DR

This paper develops an efficient semi-closed form pricing formula for discretely-sampled variance swaps within a hybrid model combining stochastic volatility and interest rates, considering full correlation effects.

Contribution

It introduces a novel semi-closed form approximation for pricing variance swaps under a complex hybrid model with full correlation, addressing non-affinity issues.

Findings

Correlation significantly impacts variance swap pricing

The proposed formula achieves accurate pricing approximations

Numerical experiments validate the model's effectiveness

Abstract

This paper considers the case of pricing discretely-sampled variance swaps under the class of equity-interest rate hybridization. Our modeling framework consists of the equity which follows the dynamics of the Heston stochastic volatility model, and the stochastic interest rate is driven by the Cox-Ingersoll-Ross (CIR) process with full correlation structure imposed among the state variables. This full correlation structure possess the limitation to have fully analytical pricing formula for hybrid models of variance swaps, due to the non-affinity property embedded in the model itself. We address this issue by obtaining an efficient semi-closed form pricing formula of variance swaps for an approximation of the hybrid model via the derivation of characteristic functions. Subsequently, we implement numerical experiments to evaluate the accuracy of our pricing formula. Our findings confirmed that the impact of the correlation between the underlying and the interest rate is significant for pricing discretely-sampled variance swaps.