Under the scenario of high-frequency data, a consistent estimator of the realized Laplace transform of volatility is proposed by Todorov and Tauchen (Econometrica 80:1105–1127, 2012) and a related central limit theorem has been well established. In this paper, we investigate the asymptotic tail behaviour of the empirical realized Laplace transform of volatility (ERLTV). We establish both a large deviation principle and a moderate deviation principle for the ERLTV. The good rate function for the large deviation principle is well defined in the whole real space, which indicates a limit for the normalized logarithmic tail probability of the ERLTV. Moreover, we also derive the function-level large and moderate deviation principles for ERLTV.

中文翻译：

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实现波动率拉普拉斯变换的大偏差原理

在高频数据场景下，Todorov 和 Tauchen (Econometrica 80:1105–1127, 2012) 提出了已实现的波动率拉普拉斯变换的一致估计量，并且已经很好地建立了相关的中心极限定理。在本文中，我们研究了经验实现的拉普拉斯波动率变换 (ERLTV) 的渐近尾行为。我们为 ERLTV 建立了大偏差原则和中度偏差原则。大偏差原理的良好速率函数在整个真实空间中被很好地定义，这表明 ERLTV 归一化对数尾概率的极限。此外，我们还推导出了 ERLTV 的函数级大中偏差原则。