The volatility characterizes the amplitude of price return fluctuations. It is a central magnitude in finance closely related to the risk of holding a certain asset. Despite its popularity on trading floors, the volatility is unobservable and only the price is known. Diffusion theory has many common points with the research on volatility, the key of the analogy being that volatility is the time-dependent diffusion coefficient of the random walk for the price return. We present a formal procedure to extract volatility from price data, by assuming that it is described by a hidden Markov process which together with the price form a two-dimensional diffusion process. We derive a maximum likelihood estimate valid for a wide class of two-dimensional diffusion processes. The choice of the exponential Ornstein-Uhlenbeck (expOU) stochastic volatility model performs remarkably well in inferring the hidden state of volatility. The formalism is applied to the Dow Jones index. The main results are: (i) the distribution of estimated volatility is lognormal, which is consistent with the expOU model; (ii) the estimated volatility is related to trading volume by a power law of the form $σ\propto V^{0.55}$; and (iii) future returns are proportional to the current volatility which suggests some degree of predictability for the size of future returns.
It is widely accepted that there is strong persistence in the volatility of financial time series. The origin of the observed persistence, or long-range memory, is still an open problem as the observed phenomenon could be a spurious effect. Earlier we have proposed the consentaneous model of the financial markets based on the non-linear stochastic differential equations. The consentaneous model successfully reproduces empirical probability and power spectral densities of volatility. This approach is qualitatively different from models built using fractional Brownian motion. In this contributio…
Effects of analyst sentiment on volatility dynamics in financial market
Ningbo University of Finance & Economics（宁波财经学院）；Wenzhou University of Technology（温州理工学院）；Fuyao University of Science and Technology（福耀科技大学）；Yunnan University（云南大学）
We study the activity, i.e., the number of transactions per unit time, of financial markets. Using the diffusion entropy technique we show that the autocorrelation of the activity is caused by the presence of peaks whose time distances are distributed following an asymptotic power law which ultimately recovers the Poissonian behavior. We discuss these results in comparison with ARCH models, stochastic volatility models and multi-agent models showing that ARCH and stochastic volatility models better describe the observed experimental evidences.
What does the financial market pricing do? A simulation analysis with a view to systemic volatility, exuberance and vagary
Biondi et al.（2012）开发了一个分析模型，以研究股票市场价格形成随时间推移的新兴动态特性，能够捕捉重要的程式化事实。这些后一种性质证明是敏感的基本信息提供的监管制度，以及对市场的信心条件之间的实际和潜在的投资者。以按市价（公允价值）计量交易证券为基础的制度虽然在市场价格和基本信号之间产生较高的线性相关性，但也涉及较高的市场不稳定性和波动性。这些制度还在市场信心空间的某些区域引发更多相关的市场繁荣和反复无常的事件，在这些区域进一步出现较低的市场流动性。
Mitigating Financial Risk from Climate-Induced Agricultural Price Volatility
Chennai Mathematical Institute（金奈数学研究所）；AI 4 Water LTD（AI for Water有限公司）；Institute for Interdisciplinary Research（跨学科研究所）；University College London（伦敦大学学院）；School of Computational & Integrative Sciences, Jawaharlal Nehru University（贾瓦哈拉尔·尼赫鲁大学计算与整合科学学院）
High quality topic extraction from business news explains abnormal financial market volatility
ETH Zurich（苏黎世联邦理工学院）；The Canon Institute for Global Studies（佳能全球战略研究所）；Swiss Finance Institute（瑞士金融研究院）；University of Tsukuba（筑波大学）；The University of Tokyo（东京大学）
