Please use this identifier to cite or link to this item: http://hdl.handle.net/2445/18833
 Title: Volatility: A hidden Markov process in financial time series Author: Eisler, ZoltánPerelló, Josep, 1974-Masoliver, Jaume, 1951- Keywords: Física matemàticaSistemes no linealsMathematical physicsNonlinear systems Issue Date: 2007 Publisher: The American Physical Society Abstract: 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, 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 a 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 forms a two-dimensional diffusion process. We derive a maximum-likelihood estimate of the volatility path 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 that (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 $\ensuremath{\sigma}\ensuremath{\propto}{V}^{0.55}$, and (iii) future returns are proportional to the current volatility, which suggests some degree of predictability for the size of future returns. Note: Reproducció del document publicat a: http://dx.doi.org/10.1103/PhysRevE.76.056105 It is part of: Physical Review E, 2007, vol. 76, núm. 5, p. 056105-1-056105-11 URI: http://hdl.handle.net/2445/18833 Related resource: http://dx.doi.org/10.1103/PhysRevE.76.056105 ISSN: 1063-651X Appears in Collections: Articles publicats en revistes (Física de la Matèria Condensada)

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