Breaks down of the modeling of the financial market with addition of non-linear terms in the Itô stochastic process

Leonardo S. Lima, S.C. Oliveira, A.F. Abeilice and J.H.C. Melgaço

Physica A: Statistical Mechanics and its Applications, 2019, vol. 526, issue C

Abstract: We analyze the effect of the inclusion of non-linear terms on Itô stochastic differential equation and analyze whether the inclusion of these terms becomes the model consistent with stylized facts obeyed by financial markets, i.e. if the model is suitable for financial market. In particular, if the inclusion of nonlinear terms destroys the character of the model as a possible mathematical model for behavior of the price dynamics of the market. We have investigated the behavior of the long-tail distribution of the volatilities and verified the inverse cubic law behavior obeyed for some financial markets. We also obtain the behavior of the long range memory and analyze whether it is into the range followed by models of the financial market.

Keywords: Stochastic differential equation; Non-linear (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:526:y:2019:i:c:s0378437119305370

DOI: 10.1016/j.physa.2019.04.168

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