A General Class of Multifractional Processes and Stock Price Informativeness

TL;DR

This paper introduces a new class of multifractional stochastic processes driven by multifractional Brownian motion, with a novel estimation method for their pointwise H"older exponents, demonstrating improved performance over existing methods and applications in modeling stock price informativeness.

Contribution

It proposes a new generalized quadratic variation approach for estimating PHEs of multifractional processes driven by mBm, outperforming benchmark methods in simulations.

Findings

The new estimator shows better accuracy in simulations.

Multifractional processes effectively model time-varying stock price roughness.

Empirical analysis reveals stock informativeness varies over time and regions.

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.