We investigate the role of realized volatility in pricing VIX options by using the generalized affine realized volatility (GARV) model, and the Realized generalized autoregressive conditionally heteroscedastic (GARCH) model. We develop a closed-form pricing formula for the (affine) GARV model. For the (nonaffine) log-linear Realized GARCH model, we introduce a novel approximation approach to derive its analytical pricing formula. Empirical results show that models with realized volatility significantly outperform competing models based on daily returns only, both in- and out-of-sample. The Realized GARCH model offers the best pricing performance, as it has fewer constraints and a more flexible modeling structure.

中文翻译：

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为具有已实现波动率的 VIX 期权定价

我们通过使用广义仿射已实现波动率 (GARV) 模型和已实现广义自回归条件异方差 (GARCH) 模型研究已实现波动率在 VIX 期权定价中的作用。我们为（仿射）GARV 模型开发了一个封闭形式的定价公式。对于（非仿射）对数线性实现 GARCH 模型，我们引入了一种新颖的近似方法来推导其分析定价公式。实证结果表明，具有已实现波动率的模型显着优于仅基于每日回报的竞争模型，无论是样本内还是样本外。Realized GARCH 模型提供了最佳的定价性能，因为它具有更少的约束和更灵活的建模结构。