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用于刻画杠杆效应和均值回归的阈值局部波动率模型

文章 arXiv papers · 作者: Antoine Lejay et al.
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总结

本文提出连续时间局部波动率模型，其漂移系数和波动率系数分段恒定。价格阈值会使动态在不同状态间切换，因此模型能够表示杠杆效应（即价格较低时波动率较高）和均值回归行为。该方法被描述为自激阈值自回归模型的连续时间类比。

文章提出了系数和阈值的估计方法。将该方法应用于多个时间窗口内的 NYSE 和S&P 500 股票日价格后，估计结果持续显示杠杆效应的证据，并且在危机期间最清晰地检测到均值回归。所报告的证据来自历史样本的实证分析；文中未提供预测或交易绩效结果，也未说明稳健性检验或实施细节。

核心观点

  • 价格阈值决定适用哪种漂移和波动率状态。
  • 该模型在连续时间价格过程中使用分段恒定系数。
  • 该框架旨在同时捕捉杠杆效应和均值回归效应。
  • 历史估计显示存在杠杆效应证据，且危机期间的均值回归更明显。

标签

股票波动率均值回归统计学美国市场
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# A threshold model for local volatility: evidence of leverage and mean reversion effects on historical data


# A threshold model for local volatility: evidence of leverage and mean reversion effects on historical data









In financial markets, low prices are generally associated with high volatilities and vice-versa, this well known stylized fact usually being referred to as leverage effect. We propose a local volatility model, given by a stochastic differential equation with piecewise constant coefficients, which accounts of leverage and mean-reversion effects in the dynamics of the prices. This model exhibits a regime switch in the dynamics accordingly to a certain threshold. It can be seen as a continuous-time version of the Self-Exciting Threshold Autoregressive (SETAR) model. We propose an estimation procedure for the volatility and drift coefficients as well as for the threshold level. Parameters estimated on the daily prices of 348 stocks of NYSE and S\&P 500, on different time windows, show consistent empirical evidence for leverageeffects. Mean-reversion effects are also detected, most markedly in crisis periods.

在遵守原作品许可的前提下，附作者信息全文展示。 许可协议: abstract CC0

此摘要由 Stratmill 研究智能体根据原文撰写，并非原文副本。