期货衍生品的多尺度随机波动模型

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英文标题：
《Multiscale Stochastic Volatility Model for Derivatives on Futures》
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作者：
Jean-Pierre Fouque, Yuri F. Saporito, Jorge P. Zubelli
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最新提交年份：
2013
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英文摘要：
  In this paper we present a new method to compute the first-order approximation of the price of derivatives on futures in the context of multiscale stochastic volatility of Fouque \\textit{et al.} (2011, CUP). It provides an alternative method to the singular perturbation technique presented in Hikspoors and Jaimungal (2008). The main features of our method are twofold: firstly, it does not rely on any additional hypothesis on the regularity of the payoff function, and secondly, it allows an effective and straightforward calibration procedure of the model to implied volatilities. These features were not achieved in previous works. Moreover, the central argument of our method could be applied to interest rate derivatives and compound derivatives. The only pre-requisite of our approach is the first-order approximation of the underlying derivative. Furthermore, the model proposed here is well-suited for commodities since it incorporates mean reversion of the spot price and multiscale stochastic volatility. Indeed, the model was validated by calibrating it to options on crude-oil futures, and it displays a very good fit of the implied volatility.
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中文摘要：
本文中，我们提出了一种新的方法，在Fouque等人（2011，CUP）的多尺度随机波动背景下，计算期货衍生品价格的一阶近似值。它为Hikspoors和Jaimungal（2008）提出的奇异摄动技术提供了一种替代方法。我们的方法的主要特点有两个：第一，它不依赖于任何关于支付函数规律性的额外假设，第二，它允许对模型进行有效且直接的隐含波动率校准。这些特性在以前的工作中没有实现。此外，我们方法的核心论点可以应用于利率衍生品和复合衍生品。我们的方法的唯一先决条件是基础导数的一阶近似。此外，本文提出的模型非常适合大宗商品，因为它包含了现货价格的均值回归和多尺度随机波动。事实上，通过将该模型与原油期货期权进行校准，该模型得到了验证，并显示出与隐含波动率非常吻合的结果。
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分类信息：

一级分类：Quantitative Finance        数量金融学
二级分类：Computational Finance        计算金融学
分类描述：Computational methods, including Monte Carlo, PDE, lattice and other numerical methods with applications to financial modeling
计算方法，包括蒙特卡罗，偏微分方程，格子和其他数值方法，并应用于金融建模
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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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关键词：波动模型 衍生品 Quantitative Perturbation volatilities