Modified Brownian Motion Approach to Modeling Returns Distribution | Zendy

Dhesi Gurjeet | Zendy; Shakeel Muhammad Bilal | Zendy; Xiao Ling | Zendy

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Modified Brownian Motion Approach to Modeling Returns Distribution

Author(s) -

Dhesi Gurjeet,

Shakeel Muhammad Bilal,

Xiao Ling

Publication year - 2016

Publication title -

wilmott

Language(s) - English

Resource type - Journals

eISSN - 1541-8286

pISSN - 1540-6962

DOI - 10.1002/wilm.10494

Subject(s) - geometric brownian motion , weighting , brownian motion , mathematics , fractional brownian motion , goodness of fit , econometrics , interpretation (philosophy) , trigonometry , extension (predicate logic) , statistical physics , computer science , diffusion process , mathematical analysis , statistics , physics , knowledge management , innovation diffusion , acoustics , programming language

An innovative extension of the geometric Brownian motion model is developed by incorporating a weighting factor and a stochastic function modeled as a mixture of power and trigonometric functions. Simulations based on this modified Brownian motion model, with optimal weighting factors selected by goodness‐of‐fit tests, substantially outperform the basic geometric Brownian motion model in terms of fitting the returns distribution of historic data price indices. Furthermore, we attempt to provide an interpretation of the additional stochastic term in relation to irrational behavior in financial markets and outline the importance of this novel model.

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