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Extreme times for volatility processes.

Jaume Masoliver1, Josep Perelló

  • 1Departament de Física Fonamental, Universitat de Barcelona, Diagonal 647, E-08028 Barcelona, Spain.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|May 16, 2007
PubMed
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Extreme times techniques reveal universal patterns in financial market volatility. Analysis of mean first-passage time in return series shows complex dynamics, differing from simple diffusion models.

Area of Science:

  • Quantitative Finance
  • Statistical Mechanics
  • Financial Market Analysis

Background:

  • Extreme value theory, typically used in statistical mechanics, offers insights into financial market dynamics.
  • Understanding the behavior of financial market volatility is crucial for risk management and economic forecasting.

Purpose of the Study:

  • To investigate the mean first-passage time of return volatility in financial markets.
  • To compare empirical findings with theoretical models, including the Wiener process and stochastic volatility models.

Main Methods:

  • Application of extreme times techniques to analyze time series data of major stock market indices.
  • Calculation and comparison of empirical mean first-passage times with predictions from stochastic volatility models.

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Main Results:

  • Empirical results suggest a universal pattern in volatility behavior across different financial indices.
  • The mean first-passage time behavior deviates significantly from the Wiener process, indicating a mean-reverting force on volatility.
  • The exponential Ornstein-Uhlenbeck model shows good agreement with empirical data.

Conclusions:

  • Financial market volatility exhibits complex, non-diffusive dynamics driven by a mean-reverting force.
  • Extreme value theory provides a valuable framework for understanding financial market behavior.
  • The exponential Ornstein-Uhlenbeck model effectively captures key aspects of financial volatility dynamics.