In this paper, we discuss the problem of pricing discretely sampled variance swaps under a hybrid stochastic model. Our modeling framework is a combination with a double Heston stochastic volatility model and a Cox–Ingersoll–Ross stochastic interest rate process. Due to the application of the T-forward measure with the stochastic interest process, we can only obtain an efficient semi-closed form of pricing formula for variance swaps instead of a closed-form solution based on the derivation of characteristic functions. The practicality of this hybrid model is demonstrated by numerical simulations.

中文翻译：

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具有随机利率的双赫斯顿随机波动率模型下的定价方差互换

在本文中，我们讨论了在混合随机模型下对离散抽样方差互换定价的问题。我们的建模框架结合了双 Heston 随机波动率模型和 Cox-Ingersoll-Ross 随机利率过程。由于 T-forward 测度与随机利率过程的应用，我们只能获得一个有效的半封闭形式的方差掉期定价公式，而不是基于特征函数推导的封闭形式的解决方案。数值模拟证明了这种混合模型的实用性。