Extreme Times for Volatility Processes

29 Pages Posted: 9 May 2007

See all articles by Josep Perelló

Josep Perelló

University of Barcelona - Department of Physics

Jaume Masoliver

University of Barcelona - Department of Physics

Date Written: May 7, 2007

Abstract

Extreme times techniques, generally applied to nonequilibrium statistical mechanical processes, are also useful for a better understanding of financial markets. We present a detailed study on the mean first-passage time for the volatility of return time series. The empirical results extracted from daily data of major indices seem to follow the same law regardless of the kind of index thus suggesting an universal pattern. The empirical mean first-passage time to a certain level L is fairly different from that of the Wiener process showing a dissimilar behavior depending on whether L is higher or lower than the average volatility. All of this indicates a more complex dynamics in which a reverting force drives volatility toward its mean value. We thus present the mean first-passage time expressions of the most common stochastic volatility models whose approach is comparable to the random diffusion description. We discuss asymptotic approximations of these models and confront them to empirical results with a good agreement with the exponential Ornstein-Uhlenbeck model.

Keywords: stochastic volatility, mean first-passage time, Exponential Ornstein Uhlenbeck

Suggested Citation

Perello, Josep and Masoliver, Jaume, Extreme Times for Volatility Processes (May 7, 2007). Available at SSRN: https://ssrn.com/abstract=984885 or http://dx.doi.org/10.2139/ssrn.984885

Josep Perello (Contact Author)

University of Barcelona - Department of Physics ( email )

Diagonal, 647
Barcelona, E-08028
Spain
+34 9 34021150 (Phone)
+34 34021149 (Fax)

Jaume Masoliver

University of Barcelona - Department of Physics ( email )

Barcelona, E-08028
Spain
00 34 3 402 11 59 (Phone)
00 34 3 402 11 49 (Fax)

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