The study focuses on extending the fast mean-reversion volatility, which was developed by the author in a previous work, to the multiscale volatility model so that it can express a well-separated time scale. The leading-order term and first-order correction terms are analytically computed using the perturbation theory based on the Lie–Trotter operator splitting method. Finally, the study is concluded by deriving the numerical results that further validate the effectiveness of the model.

中文翻译：

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多尺度波动模型下的相关对数正态随机变量

该研究的重点是将作者在之前的工作中开发的快速均值回复波动率扩展到多尺度波动率模型，以便可以表示一个很好的时间尺度。前导项和一阶校正项是使用基于Lie-Trotter算子分裂方法的扰动理论进行分析计算的。最后，通过得出进一步验证模型有效性的数值结果来结束研究。