Variance swap valuation under a Heston jump model with stochastic long-run variance and macro-liquidity feedback

Ke Wang; Jing Fu; Ren-hong Yan; Fan Lei; Ke Wang; Jing Fu; Ren-hong Yan; Fan Lei

doi:10.3934/math.2026900

AIMS Mathematics

2026, Volume 11, Issue 7: 22233-22257. doi: 10.3934/math.2026900

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Research article

Variance swap valuation under a Heston jump model with stochastic long-run variance and macro-liquidity feedback

1.
School of Science, Civil Aviation Flight University of China, No. 46, 4th Section of Nanchang Road, Guanghan City, Sichuan Province, China
2.
School of Mathematics and Statistics, Zhaotong University, Guoxue Road, Zhaoyang District, Zhaotong City, Yunnan Province, China
3.
Research Institute of Economics and Management, Southwestern University of Finance and Economics, No. 555 Liutai Avenue, Wenjiang District, Chengdu City, Sichuan Province, China

Received: 26 May 2026 Revised: 06 July 2026 Accepted: 14 July 2026 Published: 24 July 2026
MSC : 91G20

This paper develops an affine pricing framework for discretely and continuously monitored variance swaps under a Heston-type stochastic volatility model with finite-activity jumps, stochastic long-run variance, and macro-liquidity feedback. The key modeling feature is that a persistent macro-liquidity state variable enters the mean-reversion target of the spot variance process, so that liquidity conditions affect future expected quadratic variation through the variance target in addition to asset-price or liquidity-discount channels. Under the risk-neutral measure, the four-factor model remains exponentially affine. We derive the joint moment-generating function, the Riccati system, the fair strike for discretely sampled actual-return variance swaps, and the continuous-monitoring limiting strike. We also establish finite-horizon transform admissibility conditions and prove that the discrete actual-return strike converges to the continuous quadratic-variation benchmark as the monitoring mesh vanishes. Numerical experiments show that the proposed model nests the relevant no-liquidity and no-jump benchmarks, that Monte Carlo estimates remain close to the affine-transform prices, and that the macro-liquidity channel raises the benchmark fair strikes by about 1.9% when liquidity stress increases the effective long-run variance target. The results provide a tractable link between stochastic long-run variance modeling, liquidity-adjusted derivative valuation, and jump-sensitive variance swap pricing.
- variance swaps,
- stochastic Long-Run variance,
- Macro-liquidity,
- moment generating function,
- closed-form pricing
Citation: Ke Wang, Jing Fu, Ren-hong Yan, Fan Lei. Variance swap valuation under a Heston jump model with stochastic long-run variance and macro-liquidity feedback[J]. AIMS Mathematics, 2026, 11(7): 22233-22257. doi: 10.3934/math.2026900

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Abstract

This paper develops an affine pricing framework for discretely and continuously monitored variance swaps under a Heston-type stochastic volatility model with finite-activity jumps, stochastic long-run variance, and macro-liquidity feedback. The key modeling feature is that a persistent macro-liquidity state variable enters the mean-reversion target of the spot variance process, so that liquidity conditions affect future expected quadratic variation through the variance target in addition to asset-price or liquidity-discount channels. Under the risk-neutral measure, the four-factor model remains exponentially affine. We derive the joint moment-generating function, the Riccati system, the fair strike for discretely sampled actual-return variance swaps, and the continuous-monitoring limiting strike. We also establish finite-horizon transform admissibility conditions and prove that the discrete actual-return strike converges to the continuous quadratic-variation benchmark as the monitoring mesh vanishes. Numerical experiments show that the proposed model nests the relevant no-liquidity and no-jump benchmarks, that Monte Carlo estimates remain close to the affine-transform prices, and that the macro-liquidity channel raises the benchmark fair strikes by about 1.9% when liquidity stress increases the effective long-run variance target. The results provide a tractable link between stochastic long-run variance modeling, liquidity-adjusted derivative valuation, and jump-sensitive variance swap pricing.

References

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