粗糙波动率、分数随机模型与预测
文章 arXiv papers · 作者: Jim Gatheral et al.
总结
本文使用近期高频数据研究波动率随时间变化的平滑程度。研究报告称，在合理的时间尺度范围内，对数波动率近似表现为赫斯特指数很低的分数布朗运动。基于此，作者采用指数低于二分之一的分数随机波动率框架，并将其称为粗糙 FSV。
据描述，该模型与金融时间序列相符，并能改善已实现波动率预测。分析还解释了为何传统持久性检验可能将粗糙波动率过程产生的数据误判为长记忆，尽管模型本身并不具有长记忆。文中提出的一种微观结构解释，将粗糙性与高频交易及订单拆分联系起来。摘录未提供数据集、预测基准或数值业绩指标，因此无法在此独立评估所报告的预测改善及其适用范围。
核心观点
- 研究发现，对数波动率具有赫斯特指数较低的粗糙分数特征。
- 所提出的粗糙 FSV 模型采用低于二分之一的指数。
- 作者报告称，模型改善了已实现波动率预测，但摘录未提供基准细节。
- 即使数据来自粗糙波动率模型，标准持久性检验仍可能显示存在长记忆。
- 本文将波动率粗糙性与高频交易及订单拆分联系起来。
标签
全文
# Volatility is rough # Volatility is rough Estimating volatility from recent high frequency data, we revisit the question of the smoothness of the volatility process. Our main result is that log-volatility behaves essentially as a fractional Brownian motion with Hurst exponent H of order 0.1, at any reasonable time scale. This leads us to adopt the fractional stochastic volatility (FSV) model of Comte and Renault. We call our model Rough FSV (RFSV) to underline that, in contrast to FSV, H<1/2. We demonstrate that our RFSV model is remarkably consistent with financial time series data; one application is that it enables us to obtain improved forecasts of realized volatility. Furthermore, we find that although volatility is not long memory in the RFSV model, classical statistical procedures aiming at detecting volatility persistence tend to conclude the presence of long memory in data generated from it. This sheds light on why long memory of volatility has been widely accepted as a stylized fact. Finally, we provide a quantitative market microstructure-based foundation for our findings, relating the roughness of volatility to high frequency trading and order splitting.
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