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A general class of multifractional processes and stock price informativeness. (English) Zbl 1416.62473

Summary: 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.

MSC:

62M09 Non-Markovian processes: estimation
62F12 Asymptotic properties of parametric estimators
62P05 Applications of statistics to actuarial sciences and financial mathematics
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