In this article, we introduce and analyze a new methodology to estimate the volatility functions of jump diffusion models. Our methodology relies on the standard kernel estimation technique using truncated bipower increments. The relevant asymptotics are fully developed, allowing for the time span to increase as well as the sampling interval to decrease, and accommodate both stationary and nonstationary recurrent processes. We evaluate the performance of our estimators by simulation and provide some illustrative empirical analyses.

中文翻译：

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使用截断的 BIPOWER 增量估计跳跃扩散中的波动率函数

在本文中，我们介绍并分析了一种估计跳跃扩散模型的波动函数的新方法。我们的方法依赖于使用截断双幂增量的标准核估计技术。相关的渐近线得到充分发展，允许时间跨度增加以及采样间隔减少，并适应平稳和非平稳的循环过程。我们通过模拟评估估计器的性能，并提供一些说明性的经验分析。