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

Xin-Jiang He; Sha Lin; Xin-Jiang He; Sha Lin

doi:10.3934/math.20241081

AIMS Mathematics

2024, Volume 9, Issue 8: 22225-22238. doi: 10.3934/math.20241081

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Research article

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

Xin-Jiang He ^1,2,
Sha Lin ^{3
,
,}

1.
School of Economics, Zhejiang University of Technology, Hangzhou, China
2.
Institute for Industrial System Modernization, Zhejiang University of Technology, Hangzhou, China
3.
School of Finance, Zhejiang Gongshang University, Hangzhou, China

Received: 11 June 2024 Revised: 05 July 2024 Accepted: 08 July 2024 Published: 16 July 2024
MSC : 91G20

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.
- nonlinear mean reversion,
- regime switching,
- stochastic volatility,
- analytical,
- variance and volatility swaps
Citation: Xin-Jiang He, Sha Lin. Analytical formulae for variance and volatility swaps with stochastic volatility, stochastic equilibrium level and regime switching[J]. AIMS Mathematics, 2024, 9(8): 22225-22238. doi: 10.3934/math.20241081

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Abstract

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.

References

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