A Non-Linear Double Stochastic Model of Return in Financial Markets

Gontis, Vygintas; Ruseckas, Julius; Kononovičius, Aleksejus

doi:10.5772/9748

Cited by 11 publications

(35 citation statements)

References 27 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The proposed consentaneous agent-based and stochastic model of the financial markets is a result of our previous research in stochastic modeling, see references in [25,41], and agent-based modeling of herding interaction [33,34].…”

Section: Discussionmentioning

confidence: 99%

Consentaneous Agent-Based and Stochastic Model of the Financial Markets

Gontis

Kononovičius

2014

PLoS ONE

Self Cite

View full text Add to dashboard Cite

We are looking for the agent-based treatment of the financial markets considering necessity to build bridges between microscopic, agent based, and macroscopic, phenomenological modeling. The acknowledgment that agent-based modeling framework, which may provide qualitative and quantitative understanding of the financial markets, is very ambiguous emphasizes the exceptional value of well defined analytically tractable agent systems. Herding as one of the behavior peculiarities considered in the behavioral finance is the main property of the agent interactions we deal with in this contribution. Looking for the consentaneous agent-based and macroscopic approach we combine two origins of the noise: exogenous one, related to the information flow, and endogenous one, arising form the complex stochastic dynamics of agents. As a result we propose a three state agent-based herding model of the financial markets. From this agent-based model we derive a set of stochastic differential equations, which describes underlying macroscopic dynamics of agent population and log price in the financial markets. The obtained solution is then subjected to the exogenous noise, which shapes instantaneous return fluctuations. We test both Gaussian and q-Gaussian noise as a source of the short term fluctuations. The resulting model of the return in the financial markets with the same set of parameters reproduces empirical probability and spectral densities of absolute return observed in New York, Warsaw and NASDAQ OMX Vilnius Stock Exchanges. Our result confirms the prevalent idea in behavioral finance that herding interactions may be dominant over agent rationality and contribute towards bubble formation.

show abstract

Section: Discussionmentioning

confidence: 99%

Consentaneous Agent-Based and Stochastic Model of the Financial Markets

Gontis

Kononovičius

2014

PLoS ONE

Self Cite

View full text Add to dashboard Cite

show abstract

“…This provides an evidence that proposed noisy three state herding model can reproduce empirical statistics of return in financial market in very details. From our point of view this result is considerable step in stochastic modeling of financial markets in comparison with previous modeling [8,9], as incorporates microscopic model of agents and exogenous noise of information flow.…”

Section: Exogenous Information Flow Noisementioning

confidence: 87%

“…In [8,9], while relying on the empirical analysis, we have assumed that the return, r t (T ), fluctuates as instantaneous q-Gaussian noise ξ[r 0 (x), λ] with λ = 5 and driven by some stochastic process x(t). The function r 0 (x) has a linear form…”

Section: Exogenous Information Flow Noisementioning

confidence: 99%

Fluctuation analysis of the three agent groups herding model

Gontis

Kononovičius

2013

2013 22nd International Conference on Noise and Fluctuations (ICNF)

Self Cite

View full text Add to dashboard Cite

We derive a system of stochastic differential equations simulating the dynamics of the three agent groups with herding interaction. Proposed approach can be valuable in the modeling of the complex socio-economic systems with similar composition of the agents. We demonstrate how the sophisticated statistical features of the absolute return in the financial markets can be reproduced by extending the herding interaction of the agents and introducing the third agent state. As well we consider possible extension of proposed herding model introducing additional exogenous noise. Such consistent microscopic and macroscopic model precisely reproduces empirical power law statistics of the return in the financial markets. arXiv:1305.5958v1 [q-fin.ST]

show abstract

“…(5) suggests that it is possible to obtain other values of the power law exponent β as long as η ̸ = 1. In our previous work we have shown that η > 1 cases work very well for the modeling of high-frequency trading activity as well as high-frequency absolute returns of the financial markets [35,53,54], although theoretically η < 1 is also possible [34]. One can obtain the η > 1 case by considering the following modifications of GARCH(1,1) process:…”

Section: Nonlinear Garch(11) Process Generating Signals With 1/f Noisementioning

confidence: 96%