This paper introduces a modification to the affine GARCH model of Heston and Nandi (2000). The new model is designed to allow for a non-zero lower bound for the variance achieved by adding two parameters to the existing model. The affine structure of the moment-generating function is preserved at the level of variance, while an approximation is studied for log prices. The construction resembles the shifted continuous-time Heston (1993) model. Maximum likelihood estimation is performed on real data, and the model is shown to improve the fitting of the implied volatility surface, particularly for deep out-of-the-money options.

中文翻译：

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具有仿射方差的移位 GARCH 模型：定价中的应用


本文介绍了对 Heston 和 Nandi （2000） 的仿射 GARCH 模型的修改。新模型旨在允许通过向现有模型添加两个参数来实现的方差下限不为零。矩生成函数的仿射结构在方差水平上保持，而对数价格的近似值则进行研究。该结构类似于移位连续时间 Heston （1993） 模型。对真实数据进行最大似然估计，该模型被证明可以提高隐含波动率表面的拟合，特别是对于深度价外期权。