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Peer-reviewedCC BY 4.0PLOS One

Variance and volatility swap valuation with nonlinear liquidity-feedback stochastic volatility and regime switching

  • Jing Fu1
  • Ke Wang2
  1. 1School of Mathematics and Statistics, Zhaotong University, Zhaoyang, Zhaotong, Yunnan, P.R. China
  2. 2School of Science, Civil Aviation Flight University of China (CAFUC), Guanghan, Sichuan, P.R. China
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Abstract

This paper values discretely sampled variance swaps and absolute-return-based volatility swaps under regime-switching stochastic volatility and stochastic liquidity. Extending an existing stochastic-liquidity model, a quadratic liquidity-stress term shifts the variance-factor mean-reversion target. An exponential-quadratic forward transform yields pricing formulas through coupled Riccati equations and a finite-state Markov backward equation. Explicit finite-horizon sufficient conditions establish martingale and transform admissibility. Recomputed numerical experiments assess simulation agreement, integration accuracy and nested liquidity channels. Under the uncalibrated baseline parameterization, delayed variance feedback contributes more than the direct return-liquidity channel, while their cross-channel interaction is small. These conclusions concern the stated illustrative parameter settings and the specified absolute-return contract, whose payoff differs from the square root of realized variance.

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Cite

BibTeXRIS
BibTeX
@article{fu2026variance,
  title = {{Variance and volatility swap valuation with nonlinear liquidity-feedback stochastic volatility and regime switching}},
  author = {Jing Fu and Ke Wang},
  journal = {PLOS One},
  year = {2026},
  month = oct,
  doi = {10.1371/journal.pone.0355147},
  url = {https://doi.org/10.1371/journal.pone.0355147},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - Variance and volatility swap valuation with nonlinear liquidity-feedback stochastic volatility and regime switching
AU  - Jing Fu
AU  - Ke Wang
PY  - 2026
DA  - 2026/10/27
JO  - PLOS One
DO  - 10.1371/journal.pone.0355147
UR  - https://doi.org/10.1371/journal.pone.0355147
AB  - This paper values discretely sampled variance swaps and absolute-return-based volatility swaps under regime-switching stochastic volatility and stochastic liquidity. Extending an existing stochastic-liquidity model, a quadratic liquidity-stress term shifts the variance-factor mean-reversion target. An exponential-quadratic forward transform yields pricing formulas through coupled Riccati equations and a finite-state Markov backward equation. Explicit finite-horizon sufficient conditions establish martingale and transform admissibility. Recomputed numerical experiments assess simulation agreement, integration accuracy and nested liquidity channels. Under the uncalibrated baseline parameterization, delayed variance feedback contributes more than the direct return-liquidity channel, while their cross-channel interaction is small. These conclusions concern the stated illustrative parameter settings and the specified absolute-return contract, whose payoff differs from the square root of realized variance.
SN  - 1932-6203
ER  -