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Fractional Brownian Motion With Stochastic Variance: Modeling Absolute Returns In Stock Markets

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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)

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.

Suggested Citation

  • H. E. Roman & M. Porto, 2008. "Fractional Brownian Motion With Stochastic Variance: Modeling Absolute Returns In Stock Markets," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 19(08), pages 1221-1242.
    • Handle: RePEc:wsi:ijmpcx:v:19:y:2008:i:08:n:s0129183108012820
    DOI: 10.1142/S0129183108012820
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