摘要翻译：
相关随机波动率模型是Black和Scholes-Merton框架的自然延伸：这里的波动率不是一个常数，而是一个与价格对数收益相关的随机过程。目前，文献中讨论了几种随机波动率模型，不同的是随机波动率所包含的动力学特性。本文的目的是比较三个流行模型的最新结果：Vasicek模型、Heston模型和指数Ornstein-Uhlenbeck模型。我们分析了文献中已知的理论结果（波动率和收益分布、高阶矩和不同时间的相关性），以检验它们对原始数值模拟结果的预测有效性，特别注意它们再现价格的经验统计特性的能力。数值结果表明，这些模型可以保持其所有的特性，特别是在市场风险管理或期权定价等金融应用中。为了对模型进行批判性的比较，我们还对意大利股票市场的金融时间序列进行了实证分析，显示了指数Ornstein-Uhlenbeck模型捕捉波动率和对数收益概率分布的程式化事实的能力。
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英文标题：
《A Comparative Study of Stochastic Volatility Models》
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作者：
E. Cisana, L. Fermi, G. Montagna, O. Nicrosini
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最新提交年份：
2007
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分类信息：

一级分类：Quantitative Finance        数量金融学
二级分类：Statistical Finance        统计金融
分类描述：Statistical, econometric and econophysics analyses with applications to financial markets and economic data
统计、计量经济学和经济物理学分析及其在金融市场和经济数据中的应用
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一级分类：Physics        物理学
二级分类：Physics and Society        物理学与社会
分类描述：Structure, dynamics and collective behavior of societies and groups (human or otherwise). Quantitative analysis of social networks and other complex networks. Physics and engineering of infrastructure and systems of broad societal impact (e.g., energy grids, transportation networks).
社会和团体（人类或其他）的结构、动态和集体行为。社会网络和其他复杂网络的定量分析。具有广泛社会影响的基础设施和系统（如能源网、运输网络）的物理和工程。
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英文摘要：
  The correlated stochastic volatility models constitute a natural extension of the Black and Scholes-Merton framework: here the volatility is not a constant, but a stochastic process correlated with the price log-return one. At present, several stochastic volatility models are discussed in the literature, differing in the dynamics attached to the volatility. The aim of the present work is to compare the most recent results about three popular models: the Vasicek, Heston and exponential Ornstein-Uhlenbeck models. We analyzed for each of them the theoretical results known in the literature (volatility and return distribution, higher-order moments and different-time correlations) in order to test their predictive effectiveness on the outcomes of original numerical simulations, paying particular attention to their ability to reproduce empirical statistical properties of prices. The numerical results demonstrate that these models can be implemented maintaining all their features, especially in view of financial applications like market risk management or option pricing. In order to critically compare the models, we also perform an empirical analysis of financial time series from the Italian stock market, showing the exponential Ornstein-Uhlenbeck model's ability to capture the stylized facts of volatility and log-return probability distributions.
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PDF链接：
https://arxiv.org/pdf/0709.0810