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摘要翻译：
在Heston随机波动率模型的基础上，提出了一个多尺度随机波动率模型。然后用奇异的插值展开法得到欧式期权价格的近似。由此得到的定价公式是半解析的，因为它们可以用积分表示。讨论了与数值计算这些积分有关的困难，并提供了避免这些困难的技术。总的来说，我们的模型的计算复杂度与纯Heston模型相当，但我们的修正在拟合隐含波动率面方面带来了很大的灵活性。这是用数字和期权数据说明的。
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英文标题：
《A Fast Mean-Reverting Correction to Heston's Stochastic Volatility Model》
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作者：
Jean-Pierre Fouque, Matthew Lorig
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最新提交年份：
2012
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分类信息：
一级分类：Quantitative Finance 数量金融学
二级分类：Pricing of Securities 证券定价
分类描述：Valuation and hedging of financial securities, their derivatives, and structured products
金融证券及其衍生产品和结构化产品的估值和套期保值
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一级分类：Quantitative Finance 数量金融学
二级分类：General Finance 一般财务
分类描述：Development of general quantitative methodologies with applications in finance
通用定量方法的发展及其在金融中的应用
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英文摘要：
We propose a multi-scale stochastic volatility model in which a fast mean-reverting factor of volatility is built on top of the Heston stochastic volatility model. A singular pertubative expansion is then used to obtain an approximation for European option prices. The resulting pricing formulas are semi-analytic, in the sense that they can be expressed as integrals. Difficulties associated with the numerical evaluation of these integrals are discussed, and techniques for avoiding these difficulties are provided. Overall, it is shown that computational complexity for our model is comparable to the case of a pure Heston model, but our correction brings significant flexibility in terms of fitting to the implied volatility surface. This is illustrated numerically and with option data.
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PDF链接：
https://arxiv.org/pdf/1007.4366
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