FRACTIONAL BROWNIAN MOTION WITH STOCHASTIC VARIANCE: MODELING ABSOLUTE RETURNS IN STOCK MARKETS

H. E. Roman () and M. Porto ()
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H. E. Roman: Dipartimento di Fisica, Università di Milano-Bicocca, Piazza della Scienza 3, 20126 Milano, Italy
M. Porto: Institut für Festkörperphysik, Technische Universität Darmstadt, Hochschulstr. 8, 64289 Darmstadt, Germany

International Journal of Modern Physics C (IJMPC), 2008, vol. 19, issue 08, 1221-1242

Abstract: We discuss a model for simulating a long-time memory in time series characterized in addition by a stochastic variance. The model is based on a combination of fractional Brownian motion (FBM) concepts, for dealing with the long-time memory, with an autoregressive scheme with conditional heteroskedasticity (ARCH), responsible for the stochastic variance of the series, and is denoted as FBMARCH. Unlike well-known fractionally integrated autoregressive models, FBMARCH admits finite second moments. The resulting probability distribution functions have power-law tails with exponents similar to ARCH models. This idea is applied to the description of long-time autocorrelations of absolute returns ubiquitously observed in stock markets.

Keywords: Fractional Brownian motion; stochastic variance; stock markets; 89.65.Gh; 89.75.-k; 05.40.-a (search for similar items in EconPapers)
Date: 2008
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DOI: 10.1142/S0129183108012820

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