多时间尺度与随机波动率的经验模型
Multiple time scales and the empirical models for stochastic volatility
摘要：
最常见的随机波动率模型，如Ornstein-Uhlenbeck（Heston），指数波动率（Expanding）和Hull-White模型将波动率定义为马尔可夫过程。在这项工作中，我们检查的马尔可夫近似在不同的时间尺度的适用性，并将试图回答的问题，上述随机波动率模型是最现实的。为此，我们认为在短期（几天）和长期（几个月）的时间尺度的波动性作为一个马尔可夫过程，并估计它的系数的Kramers-Moyal扩展使用的数据道琼斯指数。已经发现，经验数据允许仅取定义伊藤波动率随机微分方程的形式的前两个展开系数为非零。实证结果表明，在较长的时间尺度上，实证数据支持了实证模型。在短时间尺度下，经验模型仅在波动量较小的情况下与Expanding模型一致。
英文摘要：
The most common stochastic volatility models such as the Ornstein-Uhlenbeck (OU), the Heston, the exponential OU (ExpOU) and Hull-White models define volatility as a Markovian process. In this work we check of the applicability of the Markovian approximation at separate times scales and will try to answer the question which of the stochastic volatility models indicated above is the most realistic. To this end we consider the volatility at both short (a few days) and long (a few months)time scales as a Markovian process and estimate for it the coefficients of the Kramers-Moyal expansion using the data for Dow-Jones Index. It has been found that the empirical data allow to take only the first two coefficients of expansion to be non zero that define form of the volatility stochastic differential equation of Ito. It proved to be that for the long time scale the empirical data support the ExpOU model. At the short time scale the empirical model coincides with ExpOU model for the small volatility quantities only.
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