We combine the rough Heston model and the CIR (Cox–Ingersoll–Ross) interest rate together to form a rough Heston-CIR model, so that both the rough behaviour of the volatility and the stochastic nature of the interest rate can be captured. Despite the convoluted structure and non-Markovian property of this model, it still admits a semi-analytical pricing formula for European options, the implementation of which involves solving a fractional Riccati equation. The rough Heston-CIR model is more general, taking both the rough Heston model and the Heston-CIR model as special cases. The influence of rough volatility and stochastic interest rate is shown to be significant through numerical experiments.

中文翻译：

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粗略 HESTON-CIR 模型下欧式期权的半分析定价公式

我们将粗糙的 Heston 模型和 CIR（Cox-Ingersoll-Ross）利率结合在一起形成了粗糙的 Heston-CIR 模型，从而可以捕捉到波动的粗略行为和利率的随机性。尽管该模型具有复杂的结构和非马尔可夫性质，但它仍然承认欧式期权的半解析定价公式，其实施涉及求解分数 Riccati 方程。粗糙的 Heston-CIR 模型更通用，将粗糙的 Heston 模型和 Heston-CIR 模型都作为特例。数值实验表明，粗糙波动率和随机利率的影响是显着的。