Modeling Stock Prices by Multifractional Brownian Motion: An Improved Estimation of the Pointwise Regularity

Quantitative Finance, Forthcoming

NYU Tandon Research Paper No. 1888288

Posted: 18 Jul 2011

See all articles by Sergio Bianchi

Sergio Bianchi

University of Cassino

Alexandre Pantanella

University of Cassino

Augusto Pianese

affiliation not provided to SSRN

Abstract

The paper deals with the problem of estimating the pointwise regularity of the multifractional Brownian motion, assumed as a model of the stock price dynamics. We (a) correct the shifting bias affecting a class of absolute moment-based estimators and (b) build a data-driven algorithm in order to dynamically check the local Gaussianity of the process. The estimation is therefore performed for three stock indices: the Dow Jones Industrial Average, the Footsie 100 and the Nikkei 225. Our findings show that, after the correction, the pointwise regularity fluctuates around 1/2 (the sole value consistent with the absence of arbitrage), but significant deviations are also observable.

Keywords: multifractional Brownian motion, pointwise Hölder exponent, asset price dynamics, time varying parameter, applied finance

JEL Classification: C13, C22, C51, G14

Suggested Citation

Bianchi, Sergio and Pantanella, Alexandre and Pianese, Augusto, Modeling Stock Prices by Multifractional Brownian Motion: An Improved Estimation of the Pointwise Regularity. Quantitative Finance, Forthcoming, NYU Tandon Research Paper No. 1888288, Available at SSRN: https://ssrn.com/abstract=1888288

Sergio Bianchi (Contact Author)

University of Cassino ( email )

Via S. Angelo - Campus Folcara
Dept. of Economics and Law
Cassino, 03043
Italy
+3907762994846 (Phone)
+390776393034 (Fax)

HOME PAGE: http://www.docente.unicas.it/sergio_bianchi

Alexandre Pantanella

University of Cassino ( email )

Via S. Angelo, Loc. Folcara
Cassino, Frosinone 03043
Italy

Augusto Pianese

affiliation not provided to SSRN ( email )

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