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摘要翻译：
我们考虑了以离散抽样的标的证券的实现方差为基础的衍生品的定价问题。在文献中，已实现方差通常用其连续时间极限，即潜在对数价格的二次变化来近似。在这里，我们描述了两个对象上的选项的小时间限制。我们发现它们之间的差异很大程度上取决于股票价格过程是否有跳跃。随后，我们提出了两种基于离散抽样实现方差的期权价格评估方法。其中一种方法是近似的；它是基于我们的渐近结果对二次变差的期权价格进行修正。另一种方法是精确的；它采用了一种新的随机化方法，并应用了傅里叶-拉普拉斯技术。我们对这两种方法进行了比较，并通过一些数值例子说明了我们的结果。
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英文标题：
《Asymptotic and Exact Pricing of Options on Variance》
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作者：
Martin Keller-Ressel and Johannes Muhle-Karbe
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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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一级分类：Mathematics 数学
二级分类：Probability 概率
分类描述：Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory
概率论与随机过程的理论与应用：例如中心极限定理，大偏差，随机微分方程，统计力学模型，排队论
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英文摘要：
We consider the pricing of derivatives written on the discretely sampled realized variance of an underlying security. In the literature, the realized variance is usually approximated by its continuous-time limit, the quadratic variation of the underlying log-price. Here, we characterize the small-time limits of options on both objects. We find that the difference between them strongly depends on whether or not the stock price process has jumps. Subsequently, we propose two new methods to evaluate the price of options on the discretely sampled realized variance. One of the methods is approximative; it is based on correcting prices of options on quadratic variation by our asymptotic results. The other method is exact; it uses a novel randomization approach and applies Fourier-Laplace techniques. We compare the methods and illustrate our results by some numerical examples.
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PDF链接：
https://arxiv.org/pdf/1003.5514
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