英文标题：
《Decomposition formula for rough Volterra stochastic volatility models》
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作者：
Raul Merino, Jan Posp\\\'i\\v{s}il, Tom\\\'a\\v{s} Sobotka, Tommi Sottinen
and Josep Vives
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最新提交年份：
2019
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英文摘要：
The research presented in this article provides an alternative option pricing approach for a class of rough fractional stochastic volatility models. These models are increasingly popular between academics and practitioners due to their surprising consistency with financial markets. However, they bring several challenges alongside. Most noticeably, even simple non-linear financial derivatives as vanilla European options are typically priced by means of Monte-Carlo (MC) simulations which are more computationally demanding than similar MC schemes for standard stochastic volatility models. In this paper, we provide a proof of the prediction law for general Gaussian Volterra processes. The prediction law is then utilized to obtain an adapted projection of the future squared volatility -- a cornerstone of the proposed pricing approximation. Firstly, a decomposition formula for European option prices under general Volterra volatility models is introduced. Then we focus on particular models with rough fractional volatility and we derive an explicit semi-closed approximation formula. Numerical properties of the approximation for a popular model -- the rBergomi model -- are studied and we propose a hybrid calibration scheme which combines the approximation formula alongside MC simulations. This scheme can significantly speed up the calibration to financial markets as illustrated on a set of AAPL options.
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中文摘要：
本文的研究为一类粗糙分数阶随机波动率模型提供了一种期权定价方法。由于与金融市场惊人的一致性，这些模型在学者和从业者之间越来越受欢迎。然而，它们也带来了一些挑战。最值得注意的是，即使是简单的非线性金融衍生品（如普通欧洲期权）也通常通过蒙特卡罗（MC）模拟进行定价，这比标准随机波动率模型的类似MC方案在计算上要求更高。本文证明了一般高斯-沃尔泰拉过程的预测规律。然后利用预测定律获得未来平方波动率的自适应预测，这是拟议定价近似的基石。首先，介绍了一般Volterra波动率模型下欧式期权价格的分解公式。然后，我们重点讨论了具有粗糙分数波动率的特殊模型，并推导了一个显式半闭近似公式。研究了一种流行模型——rBergomi模型的近似值的数值性质，并提出了一种混合校准方案，该方案将近似公式与MC模拟相结合。如一组AAPL选项所示，该方案可以显著加快金融市场的校准速度。
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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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