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

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.