AIMS Mathematics (Jul 2024)

Analytical formulae for variance and volatility swaps with stochastic volatility, stochastic equilibrium level and regime switching

  • Xin-Jiang He,
  • Sha Lin

DOI
https://doi.org/10.3934/math.20241081
Journal volume & issue
Vol. 9, no. 8
pp. 22225 – 22238

Abstract

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The CIR stochastic volatility model is modified to introduce nonlinear mean reversion, with the long-run volatility average as a random variable controlled by two parts being modeled through a Brownian motion and a Markov chain, respectively. This model still possesses an analytical formulation of the forward characteristic function, from which we establish variance swap prices as well as volatility swap ones with a nonlinear payoff in closed form. The numerical implementation of the two formulae demonstrates the significant impact of regime switching.

Keywords