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A General Class of Multifractional Processes and Stock Price Informativeness

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  • Qidi Peng
  • Ran Zhao

Abstract

We introduce a general class of stochastic processes driven by a multifractional Brownian motion (mBm) and study the estimation problems of their pointwise H\"older exponents (PHE) based on a new localized generalized quadratic variation approach (LGQV). By comparing our suggested approach with the other two existing benchmark estimation approaches (classic GQV and oscillation approach) through a simulation study, we show that our estimator has better performance in the case where the observed process is some unknown bivariate function of time and mBm. Such multifractional processes, whose PHEs are time-varying, can be used to model stock prices under various market conditions, that are both time-dependent and region-dependent. As an application to finance, an empirical study on modeling cross-listed stocks provides new evidence that the equity path's roughness varies via time and the stock price informativeness properties from global stock markets.

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  • Qidi Peng & Ran Zhao, 2017. "A General Class of Multifractional Processes and Stock Price Informativeness," Papers 1708.04217, arXiv.org, revised Aug 2018.
    • Handle: RePEc:arx:papers:1708.04217
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    1. Werner Antweiler & Murray Z. Frank, 2004. "Is All That Talk Just Noise? The Information Content of Internet Stock Message Boards," Journal of Finance, American Finance Association, vol. 59(3), pages 1259-1294, June.
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    Cited by:

    1. Angelini, Daniele & Bianchi, Sergio, 2023. "Nonlinear biases in the roughness of a Fractional Stochastic Regularity Model," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).

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