A jump diffusion model for VIX volatility options and futures
A jump diffusion model for VIX volatility options and futures
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DOI：
10.1007/s11156-009-0153-8
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发表时间：
2010-10
影响因子：
1.7
通讯作者：
Dimitris Psychoyios;George Dotsis;Raphael N. Markellos
中科院分区：
文献类型：
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作者：
Dimitris Psychoyios;George Dotsis;Raphael N. Markellos
波动率指数作为衡量市场不确定性的指标和开发衍生工具的新资产类别越来越受欢迎。虽然跳跃被广泛认为是波动率的一个显著特征，但其对波动率期权和期货定价的影响尚未完全理解。本文提供的证据表明，时间序列的波动率指数的行为是很好的近似的均值回复对数扩散跳跃。这个过程能够捕捉VIX动态的程式化事实，例如在较高水平的快速均值回归，波动性的水平效应和市场压力时期的大幅上行。基于实证结果，我们分别给出了基于即期和远期波动率指数的欧式期权定价模型。
Volatility indices are becoming increasingly popular as a measure of market uncertainty and as a new asset class for developing derivative instruments. Although jumps are widely considered as a salient feature of volatility, their implications for pricing volatility options and futures are not yet fully understood. This paper provides evidence indicating that the time series behaviour of the VIX index is well approximated by a mean reverting logarithmic diffusion with jumps. This process is capable of capturing stylized facts of VIX dynamics such as fast mean-reversion at higher levels, level effects of volatility and large upward movements during times of market stress. Based on the empirical results, we provide closed-form valuation models for European options written on the spot and forward VIX, respectively.