The class of nonlinear stochastic models as a background for the bursty behavior in financial markets

TL;DR

This paper explores nonlinear stochastic models with multiplicative noise to explain bursty behavior in financial market returns, deriving burst duration distributions and confirming results through numerical simulations.

Contribution

It introduces a nonlinear SDE framework transforming into a Bessel process, providing analytical burst duration PDFs and applying them to financial market data.

Findings

Derived analytical PDF of burst durations

Confirmed analytical results with numerical simulations

Applied model to financial market return data

Abstract

We investigate large changes, bursts, of the continuous stochastic signals, when the exponent of multiplicativity is higher than one. Earlier we have proposed a general nonlinear stochastic model which can be transformed into Bessel process with known first hitting (first passage) time statistics. Using these results we derive PDF of burst duration for the proposed model. We confirm analytical expressions by numerical evaluation and discuss bursty behavior of return in financial markets in the framework of modeling by nonlinear SDE.