We introduce a general class of stochastic processes driven by a multifractional Brownian motion (mBm) and study  estimation problems of their pointwise H\"older exponents (PHE) based on a new localized generalized quadratic variation approach  . By comparing our suggested approach with the other two existing benchmark estimation approaches ( classicial LGQV 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. The time-varying feature of the PHE allows us to apply such class of multifractional processes 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  stock price informativeness properties from global stock markets.
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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classicial LGQV
classic GQV
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Such multifractional processes, whose PHEs are
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feature of the PHE allows us to apply such class of multifractional processes
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