Autore
Frezza, Massimiliano

Titolo
A stochastic modelling of the memory function of multifractional Brownian motion
Periodico
Università degli studi di Cassino. Dipartimento Istituzioni, Metodi Quantitativi e Territorio (DIMeT). Quaderni di Ricerca
Anno: 2008 - Volume: 4 - Fascicolo: 3 - Pagina iniziale: 1 - Pagina finale: 21

We propose a stochastic model in order to describe the memory function’s behaviour of Multifractional Brownian motion via the square root Ornstein-Uhlenbeck process (O.U.). We provide a stochastic process for capturing the H(t)’s (Hölderian function) dynamics exploiting a particular stochastic di¤erential equation (SDE) underlining the H(t)’s mean-reverting movement. Furthermore, assuming this process for the H(t)’s path, empirical evidences about the stock indexes structure and about the stock indexes level of (in)e¢ ciency are o¤ered analyzing the dynamics of four market indexes. Keywords: (Multi)fractional Brownian motion, LRD estimators, stochastic differential equations, Ornstein-Uhlenbeck process.



Testo completo: http://dimet.eco.unicas.it/files/paper%20Frezza%20copia.pdf

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