新兴市场价格指数典型波动的内在动力学：从分钟到月的赫斯顿模型
Underlying Dynamics of Typical Fluctuations of an Emerging Market Price Index: The Heston Model from Minutes to Months
摘要：
我们研究了具有随机波动率和指数尾的Heston模型作为巴西圣保罗证券交易所指数（IBOVESPA）的典型价格波动模型。首先对原材料价格进行通货膨胀修正，然后选择一个以无记忆回报为特征的15年期进行分析。通过观察波动率标度和相关性来估计模型参数。我们发现，赫斯顿模型的波动率均值回复动态至少有两个时间尺度令人满意地描述了从大于20分钟到160天的时间尺度的价格波动。在小于20分钟的时间尺度上，我们观察到自相关收益率和与赫斯顿模型不兼容的幂律尾部。尽管巴西市场在研究期间经历了重大的监管变化、恶性通货膨胀和货币危机，但所提供的描述的总体成功可以被视为赫斯顿模型很好地近似的中间宏观经济时间尺度上价格波动的一般基本动态的证据。我们还注意到，赫斯顿模型和埃克塞特模型之间的联系可以被利用，为微观经济市场机制带来新的见解。
英文摘要：
We investigate the Heston model with stochastic volatility and exponential tails as a model for the typical price fluctuations of the Brazilian São Paulo Stock Exchange Index (IBOVESPA). Raw prices are first corrected for inflation and a period spanning 15 years characterized by memoryless returns is chosen for the analysis. Model parameters are estimated by observing volatility scaling and correlation properties. We show that the Heston model with at least two time scales for the volatility mean reverting dynamics satisfactorily describes price fluctuations ranging from time scales larger than 20 minutes to 160 days. At time scales shorter than 20 minutes we observe autocorrelated returns and power law tails incompatible with the Heston model. Despite major regulatory changes, hyperinflation and currency crises experienced by the Brazilian market in the period studied, the general success of the description provided may be regarded as an evidence for a general underlying dynamics of price fluctuations at intermediate mesoeconomic time scales well approximated by the Heston model. We also notice that the connection between the Heston model and Ehrenfest urn models could be exploited for bringing new insights into the microeconomic market mechanics.
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