Chaotic behavior in financial market volatility

Litimi, Houda; BenSaïda, Ahmed; Belkacem, Lotfi; Abdallah, Oussama

doi:10.21314/jor.2018.400

Cited by 8 publications

(6 citation statements)

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“…Garcin and Guégan [ 61 ] adapted the theory for signals in which the noise influence is nonlinear and the wavelet transform-based detection of chaos has been proposed by Rubežić et al [ 62 ]. While this approach could be appropriate for physical systems where noise is an intruder of the real pure signal, for financial data, where noise is an inherent property to markets, denoising the data could modify some of the stylized financial facts that have been discussed earlier in the paper and alter the true dynamics that underlie the time series to be tested [ 63 ]. Hence, following this reasoning, a neural network approach has been chosen in this research.…”

Section: Methodsmentioning

confidence: 99%

A Comprehensive Framework for Uncovering Non-Linearity and Chaos in Financial Markets: Empirical Evidence for Four Major Stock Market Indices

Inglada-Pérez

2020

Entropy

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The presence of chaos in the financial markets has been the subject of a great number of studies, but the results have been contradictory and inconclusive. This research tests for the existence of nonlinear patterns and chaotic nature in four major stock market indices: namely Dow Jones Industrial Average, Ibex 35, Nasdaq-100 and Nikkei 225. To this end, a comprehensive framework has been adopted encompassing a wide range of techniques and the most suitable methods for the analysis of noisy time series. By using daily closing values from January 1992 to July 2013, this study employs twelve techniques and tools of which five are specific to detecting chaos. The findings show no clear evidence of chaos, suggesting that the behavior of financial markets is nonlinear and stochastic.

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Section: Methodsmentioning

confidence: 99%

A Comprehensive Framework for Uncovering Non-Linearity and Chaos in Financial Markets: Empirical Evidence for Four Major Stock Market Indices

Inglada-Pérez

2020

Entropy

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“…On the contrary, positive Lyapunov exponents describe a dispersion in phase space [63]. When the Lyapunov exponent grows, the sensitivity of the system reacts rapidly to the change of its starting conditions.…”

Section: The Lyapunov Exponentmentioning

confidence: 99%

Portfolio selection and fractal market hypothesis: Evidence from the London stock exchange

Aygören¹,

Uyar²

2023

Pamukkale J Eng Sci

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It is well known that the models supporting the Modern Portfolio Theory (MPT) and the Efficient Market Hypothesis (EMH) are constructed in the framework of random walk theory. However, a large and growing literature criticizes those models. The Fractal Market Hypothesis (FMH) was proposed as an alternative hypothesis to EMH. The motivation of this study is Peters ' [45,46] works that examine the portfolio selection case based on the non-normality framework. The aim of the study is to propose a new approach to theoretical framework of portfolio selection in terms of FMH. Daily observations of 92 stocks traded in London Stock Exchange are used to investigate the fractal behavior. Thus, the Hurst exponents as a means of indicator of a fractal structure are calculated for simulated portfolios. Results of the analysis show that the validity of MPT and EMH is questionable in London Stock Exchange. To examine the relationship between Hurst exponents (as a measure of risk) and returns, scattered diagrams are constructed for 5000 simulated portfolios. Existence of a pattern with a frontier is detected that may enable investors to optimize their portfolios. Further, The Hurst exponents of efficient frontier portfolios of Markowitz are calculated in order to investigate whether there is any linkage with the frontier of simulated portfolios. The results show that major deviations occur between these two frontiers. To understand these deviations, the Lyapunov exponents are suggested for detailed information. As a conclusion, it is recommended that investors should calculate an optimal solution with regards to the Hurst and Lyapunov exponents to maximize their returns. Peters'ın [45,46] portföy seçimini normal dağılıma uymayan çerçevede inceleyen çalışmalarına dayanmaktadır. Çalışmanın amacı, portföy seçiminin teorik çerçevesine FMH açısından yeni bir yaklaşım önermektir. Çalışmada, fraktal davranışı araştırmak için Londra Menkul Kıymetler Borsası'nda işlem gören 92 hisse senedinin günlük gözlemleri kullanılmıştır. Analizlerde, öncelikle simüle edilmiş portföyler için fraktal yapının bir göstergesi olarak Hurst üsleri hesaplanmıştır. Bulgular, Londra Menkul Kıymetler Borsası'nda MPT ve EMH'nin geçerliliğinin sorgulanabilir olduğunu göstermektedir. Getiriler ve bir risk ölçüsü olarak Hurst üsleri arasındaki ilişkiyi incelemek için 5000 simüle edilmiş portföy oluşturulmuştur. Daha sonra, simüle adilmiş portföyler üzerinde yatırımcıların getirilerini optimize etmelerini sağlayabilecek bir etkin sınırın varlığı tespit edilmiştir. Sonuçları detaylı incelemek amacıyla, simüle edilmiş etkin sınır ile Markowitz'in etkin sınır portföylerinin Hurst üsleri hesaplanmıştır ve karşılaştırmalar yapılmıştır. Sonuçta, bu iki etkin sınır arasında büyük sapmaların meydana geldiğini tespit edilmiştir. Son olarak, sapmaların davranışlarını anlamak için Lyapunov üsleri kullanılmıştır. Araştırma sonucunda, yatırımcıların getirilerini maksimize etmek için Hurst ve Lyapunov üslerine göre optimal bir çözüm hesaplamaları önerilmiştir. Modern Portföy T...

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“…This suggests that this methodology could be useful for modeling a wide variety of nonlinear and heavy-tailed time series. Since Litimi et al (2019) have recently demonstrated that chaos is likely to be present in financial market volatility, these simulation results are potentially directly relevant to financial applications. In the next section we will present an empirical application to financial market data where the modeling method can achieve similar predictive performance to that shown in Table 2.…”

Section: Simulation: Lorenz-driven Volatilitymentioning

confidence: 99%

Dynamic tail inference with log-Laplace volatility

Chavez

2019

Preprint

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We propose a family of models that enable predictive estimation of time-varying extreme event probabilities in heavy-tailed and nonlinearly dependent time series. The models are a white noise process with conditionally log-Laplace stochastic volatility. In contrast to other, similar stochastic volatility formalisms, this process has analytic expressions for its conditional probabilistic structure that enable straightforward estimation of dynamically changing extreme event probabilities. The process and volatility are conditionally Pareto-tailed, with tail exponent given by the reciprocal of the log-volatility's mean absolute innovation. This formalism can accommodate a wide variety of nonlinear dependence, as well as conditional power law-tail behavior ranging from weakly non-Gaussian to Cauchy-like tails. We provide a computationally straightforward estimation procedure that uses an asymptotic approximation of the process' dynamic large deviation probabilities. We demonstrate the estimator's utility with a simulation study. We then show the method's predictive capabilities on a simulated nonlinear time series where the volatility is driven by the chaotic Lorenz system. Lastly we provide an empirical application, which shows that this simple modeling method can be effectively used for dynamic and predictive tail inference in financial time series.

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Chaotic behavior in financial market volatility

Cited by 8 publications

References 0 publications

A Comprehensive Framework for Uncovering Non-Linearity and Chaos in Financial Markets: Empirical Evidence for Four Major Stock Market Indices

A Comprehensive Framework for Uncovering Non-Linearity and Chaos in Financial Markets: Empirical Evidence for Four Major Stock Market Indices

Portfolio selection and fractal market hypothesis: Evidence from the London stock exchange

Dynamic tail inference with log-Laplace volatility

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