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摘要翻译：
研究了随机波动率模型下的期权定价问题，重点讨论了指数Ornstein-Uhlenbeck过程和Stein-Stein过程的线性逼近。实际上，我们证明了它们在波动率过程的低波动状态下具有相同的极限动力学，在此条件下我们导出了与风险中性概率密度相关的特征函数的精确表达式。这个表达式允许我们利用Lewis和Lipton导出的公式计算期权价格。我们详细分析了普通普通股票的情况，这些股票是可以获得可靠隐含波动率表面的液体工具。我们还计算了前四个累积量的解析表达式，这是实现简单的两步校准过程的关键。它已经通过米兰证券交易所交易的一组期权数据进行了测试。数据分析表明，与市场隐含曲面拟合良好，并验证了线性逼近的准确性。
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英文标题：
《Option pricing under Ornstein-Uhlenbeck stochastic volatility: a linear
model》
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作者：
Giacomo Bormetti, Valentina Cazzola, Danilo Delpini
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最新提交年份：
2010
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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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英文摘要：
We consider the problem of option pricing under stochastic volatility models, focusing on the linear approximation of the two processes known as exponential Ornstein-Uhlenbeck and Stein-Stein. Indeed, we show they admit the same limit dynamics in the regime of low fluctuations of the volatility process, under which we derive the exact expression of the characteristic function associated to the risk neutral probability density. This expression allows us to compute option prices exploiting a formula derived by Lewis and Lipton. We analyze in detail the case of Plain Vanilla calls, being liquid instruments for which reliable implied volatility surfaces are available. We also compute the analytical expressions of the first four cumulants, that are crucial to implement a simple two steps calibration procedure. It has been tested against a data set of options traded on the Milan Stock Exchange. The data analysis that we present reveals a good fit with the market implied surfaces and corroborates the accuracy of the linear approximation.
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PDF链接：
https://arxiv.org/pdf/0905.1882
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