A scaled version of the double-mean-reverting model for VIX derivatives

Jeonggyu Huh; Jaegi Jeon; Jeong-Hoon Kim

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A scaled version of the double-mean-reverting model for VIX derivatives

机译：VIX衍生品的均值回复模型的缩放版本

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摘要

As the Heston model is not consistent with VIX data in real market well enough, alternative stochastic volatility models including the double-mean-reverting model of Gatheral (in: Bachelier Congress, 2008) have been developed to overcome its limitation. The double-mean-reverting model is a three factor model successfully reflecting the empirical dynamics of the variance but there is no closed form solution for VIX derivatives and SPX options and thus calibration using conventional techniques may be slow. In this paper, we propose a fast mean-reverting version of the double-mean-reverting model. We obtain a closed form approximation for VIX derivatives and show how it is effective by comparing it with the Heston model and the double-mean-reverting model.

机译：由于Heston模型与实际市场中的VIX数据不够吻合，因此已经开发了替代的随机波动率模型，包括Gatheral的双均值回复模型（见Bachelier Congress，2008年），以克服其局限性。双均值回复模型是一个三因素模型，成功地反映了方差的经验动态，但没有VIX导数和SPX选项的闭式解，因此使用常规技术进行的校准可能很慢。在本文中，我们提出了双均值回复模型的快速均值回复版本。我们获得了VIX导数的闭式近似值，并通过将其与Heston模型和双重均值回归模型进行比较来显示其有效性。

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来源
《Mathematics and financial economics》 |2018年第4期|495-515|共21页
作者
Jeonggyu Huh; Jaegi Jeon; Jeong-Hoon Kim;
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作者单位

Department of Mathematics, Yonsei University;

Department of Mathematics, Yonsei University;

Department of Mathematics, Yonsei University;

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原文格式 PDF
正文语种 eng
中图分类
关键词
VIX derivatives; Heston’s volatility; Double-mean-reverting volatility; Calibration;

机译：VIX衍生工具;赫斯顿波幅;两次均值恢复波幅;校准;

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A scaled version of the double-mean-reverting model for VIX derivatives

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