Autore: Frezza, Massimiliano
Titolo: Modelling price movements via the multifractional Brownian motion
Periodico: Università degli studi di Cassino. Dipartimento Istituzioni, Metodi Quantitativi e Territorio (DIMeT). Quaderni di Ricerca
Anno: 2009 - Volume: 5 - Fascicolo: 4 - Pagina iniziale: 1 - Pagina finale: 23

We show empirically how the Multifractional Brownian motion (mBm), recently introduced by Péltier and Lévy Véhel (1995) as a generalization of the well-known Fractional Brownian motion(Mandelbrot-Van Ness 1968), is more suitable in order to describe the financial log-price variations with respect to traditional methods. To test its capacity to replicate the price movements, the distributional properties of the mBm are compared with two stochastic processes widely used in…nance: 1) the Generalized Wiener Process (gWp, classical approach to …nancial markets); 2) the Generalized autoregressive conditional heteroschedasticity model (Garch model, Bollerslev 1986). By analysing the performance of six international market indexes, we will show that this new kind of Brownian approach is more e¤ective (especially when the market is higly volatile), than usual approaches. The method choosen for the estimates of the Hölderian function H (t) (the core of the mBm) is the "sliding window" technique, introduced by Bianchi in 2005. Keywords: (Multi)fractional Brownian motion; Garch models; conditional heteroschedastic variance, financial markets.


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

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