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Noncompartmental Analysis: Statistical Moment Theory00:56

Noncompartmental Analysis: Statistical Moment Theory

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Random Variables01:09

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Standard Deviation01:10

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The most commonly used measure of variation is the standard deviation. It is a numerical value measuring how far data values are from their mean. The standard deviation value is small when the data are concentrated close to the mean, exhibiting slight variation or spread. The standard deviation value is never negative, it is either positive or zero. The standard deviation is larger when the data values are more spread out from the mean, which means the data values are exhibiting more...
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Related Experiment Video

Updated: Jul 7, 2026

Measuring the Subjective Value of Risky and Ambiguous Options using Experimental Economics and Functional MRI Methods
13:04

Measuring the Subjective Value of Risky and Ambiguous Options using Experimental Economics and Functional MRI Methods

Published on: September 19, 2012

Volatility: a hidden Markov process in financial time series.

Zoltán Eisler1, Josep Perelló, Jaume Masoliver

  • 1Department of Theoretical Physics, Budapest University of Technology and Economics, Budafoki út 8., H-1111, Budapest, Hungary. eisler@maxwell.phy.bme.hu

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|February 1, 2008
PubMed
Summary

This study introduces a novel method to estimate unobservable financial volatility from price data. The approach reveals volatility

Related Experiment Videos

Last Updated: Jul 7, 2026

Measuring the Subjective Value of Risky and Ambiguous Options using Experimental Economics and Functional MRI Methods
13:04

Measuring the Subjective Value of Risky and Ambiguous Options using Experimental Economics and Functional MRI Methods

Published on: September 19, 2012

Area of Science:

  • Quantitative Finance
  • Financial Econometrics
  • Stochastic Processes

Background:

  • Volatility, a key measure of asset risk, is unobservable and must be inferred from price data.
  • Existing methods often struggle with the dynamic and hidden nature of volatility.
  • Diffusion theory provides a framework for understanding price movements and volatility.

Purpose of the Study:

  • To develop a formal procedure for extracting the volatility path from price data.
  • To model volatility as a hidden Markov process within a two-dimensional diffusion framework.
  • To apply and validate the method using real-world financial data, specifically the Dow Jones index.

Main Methods:

  • Formulating volatility as a hidden Markov process, creating a two-dimensional diffusion process with price.
  • Deriving a maximum-likelihood estimate for the volatility path.
  • Utilizing the exponential Ornstein-Uhlenbeck (expOU) stochastic volatility model for hidden state inference.

Main Results:

  • The estimated volatility distribution follows a lognormal pattern, aligning with the expOU model.
  • A power-law relationship (sigma proportional to V^0.55) was found between estimated volatility and trading volume.
  • A positive correlation between current volatility and future returns suggests predictability.

Conclusions:

  • The developed method effectively estimates the hidden volatility path from price data.
  • The findings support the lognormal distribution of volatility and its relationship with trading volume.
  • The study indicates that current volatility may predict the magnitude of future returns, offering insights into risk management.