Model-implied valuation of variance and scaled absolute-return swaps under double-Heston volatility and stochastic liquidity

Jing Fu; Ke Wang; Jing Fu; Ke Wang

doi:10.3934/math.20261283

AIMS Mathematics

2026, Volume 11, Issue 10: 32671-32713. doi: 10.3934/math.20261283

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Research article

Model-implied valuation of variance and scaled absolute-return swaps under double-Heston volatility and stochastic liquidity

Jing Fu ¹,
Ke Wang ^{2
,
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1.
School of Mathematics and Statistics, Zhaotong University, Guoxue Road, Zhaoyang District, Zhaotong City, Yunnan Province, China
2.
School of Science, Civil Aviation Flight University of China (CAFUC), No. 46, 4th Section of Nanchang Road, Guanghan City, Sichuan Province, China

Received: 08 July 2026 Revised: 28 September 2026 Accepted: 29 September 2026 Published: 09 October 2026
MSC : 91G20, 91G60, 60H10

We study discretely monitored variance and scaled absolute-return swaps under double-Heston stochastic volatility with an Ornstein-Uhlenbeck liquidity state. Under a selected equivalent martingale measure, a forward characteristic function yields semi-closed-form valuations and connects the discrete contracts to their continuous-monitoring limits under stated moment and uniform-integrability conditions. Analytical decompositions identify the liquidity contribution and maturity-slope criteria. A short-monitoring expansion separates dispersion and leverage effects, explaining how greater volatility of variance can locally lower a discrete variance strike. A single-factor comparator matched in aggregate variance levels and initial local moments isolates maturity-dependent effects of the second persistence scale. The transform uses established affine and quadratic-affine methodology; the analysis concerns the joint role of factor allocation, liquidity transmission, and monitoring. Monte Carlo simulation, Fourier refinement, and independent normal and Heston benchmarks support numerical consistency. Liquidity-on/off comparisons and factor-risk-premium scenarios quantify dependence on the pricing specification. The absolute-return contract is a volatility proxy distinct from a conventional square-root realized-variance swap. The results provide conditional model-implied valuations with illustrative parameters; market calibration and feasible hedging remain separate questions.
- variance swap,
- scaled absolute-return swap,
- double-Heston model,
- stochastic liquidity,
- forward characteristic function,
- discrete sampling
Citation: Jing Fu, Ke Wang. Model-implied valuation of variance and scaled absolute-return swaps under double-Heston volatility and stochastic liquidity[J]. AIMS Mathematics, 2026, 11(10): 32671-32713. doi: 10.3934/math.20261283

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Abstract

We study discretely monitored variance and scaled absolute-return swaps under double-Heston stochastic volatility with an Ornstein-Uhlenbeck liquidity state. Under a selected equivalent martingale measure, a forward characteristic function yields semi-closed-form valuations and connects the discrete contracts to their continuous-monitoring limits under stated moment and uniform-integrability conditions. Analytical decompositions identify the liquidity contribution and maturity-slope criteria. A short-monitoring expansion separates dispersion and leverage effects, explaining how greater volatility of variance can locally lower a discrete variance strike. A single-factor comparator matched in aggregate variance levels and initial local moments isolates maturity-dependent effects of the second persistence scale. The transform uses established affine and quadratic-affine methodology; the analysis concerns the joint role of factor allocation, liquidity transmission, and monitoring. Monte Carlo simulation, Fourier refinement, and independent normal and Heston benchmarks support numerical consistency. Liquidity-on/off comparisons and factor-risk-premium scenarios quantify dependence on the pricing specification. The absolute-return contract is a volatility proxy distinct from a conventional square-root realized-variance swap. The results provide conditional model-implied valuations with illustrative parameters; market calibration and feasible hedging remain separate questions.

References

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