Volatility swaps valuation under stochastic volatility with jumps and stochastic intensity

TL;DR

This paper develops a new pricing formula for volatility swaps considering stochastic volatility, jumps, and stochastic intensity, using advanced mathematical techniques and numerical simulations to enhance accuracy in derivative valuation.

Contribution

It introduces a novel model incorporating jumps and stochastic intensity into volatility swap pricing and derives explicit formulas using Feynman-Kac and transform methods.

Findings

Derived a joint moment generating function for the model

Provided pricing formulas for discrete and continuous sampling

Numerical simulations validate the theoretical results

Abstract

In this paper, a pricing formula for volatility swaps is delivered when the underlying asset follows the stochastic volatility model with jumps and stochastic intensity. By using Feynman-Kac theorem, a partial integral differential equation is obtained to derive the joint moment generating function of the previous model. Moreover, discrete and continuous sampled volatility swap pricing formulas are given by employing transform techniques and the relationship between two pricing formulas is discussed. Finally, some numerical simulations are reported to support the results presented in this paper.