A general class of multifractional processes and stock price informativeness. (October 2018)

• Record Type: Journal Article
• Authors: Peng, Qidi; Zhao, Ran
• Is Part Of: Chaos, solitons and fractals. Volume 115(2018)
• Page Start: 248
• Page End: 267
• Publication Date: 2018-10
• Subjects: Multifractional processes -- Pointwise Hölder exponent -- LGQV estimation -- Stock price informativeness; 62F10 -- 62F12 -- 62M86; Chaotic behavior in systems -- Periodicals; Solitons -- Periodicals; Fractals -- Periodicals; Chaotic behavior in systems; Fractals; Solitons; Periodicals; 003.7
• DOI: 10.1016/j.chaos.2018.08.004
• Languages: English
• ISSNs: 0960-0779

Abstract

Abstract: We introduce a general class of stochastic processes driven by a multifractional Brownian motion (mBm) and study the estimation problems of their pointwise Hölder 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 approach 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 so does the corresponding stock price informativeness properties from global stock markets.