dorsal/arxiv
View SchemaVolatility: a hidden Markov process in financial time series
| Authors | Zoltan Eisler, Josep Perello, Jaume Masoliver |
|---|---|
| Categories | |
| ArXiv ID | physics/0612084 |
| URL | https://arxiv.org/abs/physics/0612084 |
| DOI | 10.1103/PhysRevE.76.056105 |
| Journal | Physical Review E 76 (2007) 056105. |
Abstract
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 $\sigma \propto V^{0.55}$; and (iii) future returns are proportional to the current volatility which suggests some degree of predictability for the size of future returns.
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"abstract": "The volatility characterizes the amplitude of price return fluctuations. It\nis a central magnitude in finance closely related to the risk of holding a\ncertain asset. Despite its popularity on trading floors, the volatility is\nunobservable and only the price is known. Diffusion theory has many common\npoints with the research on volatility, the key of the analogy being that\nvolatility is the time-dependent diffusion coefficient of the random walk for\nthe price return. We present a formal procedure to extract volatility from\nprice data, by assuming that it is described by a hidden Markov process which\ntogether with the price form a two-dimensional diffusion process. We derive a\nmaximum likelihood estimate valid for a wide class of two-dimensional diffusion\nprocesses. The choice of the exponential Ornstein-Uhlenbeck (expOU) stochastic\nvolatility model performs remarkably well in inferring the hidden state of\nvolatility. The formalism is applied to the Dow Jones index. The main results\nare: (i) the distribution of estimated volatility is lognormal, which is\nconsistent with the expOU model; (ii) the estimated volatility is related to\ntrading volume by a power law of the form $\\sigma \\propto V^{0.55}$; and (iii)\nfuture returns are proportional to the current volatility which suggests some\ndegree of predictability for the size of future returns.",
"arxiv_id": "physics/0612084",
"authors": [
"Zoltan Eisler",
"Josep Perello",
"Jaume Masoliver"
],
"categories": [
"physics.soc-ph",
"physics.data-an",
"q-fin.ST"
],
"doi": "10.1103/PhysRevE.76.056105",
"journal_ref": "Physical Review E 76 (2007) 056105.",
"title": "Volatility: a hidden Markov process in financial time series",
"url": "https://arxiv.org/abs/physics/0612084"
},
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