Dipartimento di Fisica e Chimica, Group of Interdisciplinary Theoretical Physics and CNISM, Università di Palermo, Viale delle Scienze, Edificio 18, I-90128 Palermo, Italy.
IBIM-CNR Istituto di Biomedicina ed Immunologia Molecolare "Alberto Monroy," Via Ugo La Malfa 153, I-90146 Palermo, Italy.
Phys Rev E. 2018 Jun;97(6-1):062307. doi: 10.1103/PhysRevE.97.062307.
In financial markets, greater volatility is usually considered to be synonymous with greater risk and instability. However, large market downturns and upturns are often preceded by long periods where price returns exhibit only small fluctuations. To investigate this surprising feature, here we propose using the mean first hitting time, i.e., the average time a stock return takes to undergo for the first time a large negative (crashes) or positive variation (rallies), as an indicator of price stability, and relate this to a standard measure of volatility. In an empirical analysis of daily returns for 1071 stocks traded in the New York Stock Exchange, we find that this measure of stability displays nonmonotonic behavior, with a maximum, as a function of volatility. Also, we show that the statistical properties of the empirical data can be reproduced by a nonlinear Heston model. This analysis implies that, contrary to conventional wisdom, not only high, but also low volatility values can be associated with higher instability in financial markets. This proposed measure of stability can be extremely useful in risk control.
在金融市场中，通常认为较大的波动性意味着更大的风险和不稳定性。然而，大的市场下跌和上涨往往先于很长一段时间，在这段时间内价格回报只显示出小的波动。为了研究这一令人惊讶的特征，我们在这里提出使用平均首次到达时间，即股票收益首次经历大幅负向（崩盘）或正向变化（反弹）所需的平均时间，作为价格稳定性的指标，并将其与波动性的标准衡量指标联系起来。在对纽约证券交易所交易的 1071 只股票的日回报进行的实证分析中，我们发现这种稳定性衡量指标表现出非单调行为，作为波动性的函数，存在最大值。此外，我们还表明，经验数据的统计特性可以通过非线性 Heston 模型来复制。这一分析表明，与传统观点相反，不仅高波动性，而且低波动性也可能与金融市场的更高不稳定性相关。这种稳定性的衡量标准在风险控制中非常有用。
