Financial markets’ deterministic aspects modeled by a low-dimensional equation

Orlando, Giuseppe; Bufalo, Michele; Stoop, Ruedi

doi:10.1038/s41598-022-05765-z

Cited by 17 publications

(20 citation statements)

References 77 publications

(66 reference statements)

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“…As empirically investigated in Orlando and Bufalo, 3 returns, either standardized or not, do not seem to be unconditionally normally distributed. They often show a significant amount of skewness and extra‐kurtosis 4‐7 . Skew normal distributions were first introduced by Azzalini 8 and Henze 9 and have gained some momentum because of their suitability in modeling real data.…”

Section: Literature Reviewmentioning

confidence: 99%

“…They often show a significant amount of skewness and extra-kurtosis. [4][5][6][7] Skew normal distributions were first introduced by Azzalini 8 and Henze 9 and have gained some momentum because of their suitability in modeling real data. In fact, a few years later, Kim 10 further enhanced the framework by introducing t-skew distribution as scale mixtures of skew-normal distributions.…”

Section: On the Distribution Of Returnsmentioning

confidence: 99%

“…where 𝛿 satisfies relation (5), and W 1 (t) and W 2 (t) are independent Brownian motions. From this point forward, our skew-Brownian process X(t) refers to Equation (11) (which complies with Definition 3, obviously).…”

Section: Definitionmentioning

confidence: 99%

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Forecasting portfolio returns with skew‐geometric Brownian motions

Bufalo

Liseo

Orlando

2022

Appl Stoch Models Bus & Ind

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The gist of this work is to propose a minimum tracking error portfolio that could be adopted not only as an automated alternative to ETFs but, it could also be potentially used to anticipate market changes in the target index. This goal has been achieved by adopting skew Brownian motion as a general framework.The proposed solution has been declined in two versions: the case in which the constituents (i.e., in our case the subindices) of the objective portfolio are uncorrelated among each other, and the case in which correlation should be taken into account. Our tests, carried out on the S&P 500, as an example of a developed market, and Bovespa, as an example of an emerging market, shows that the proposed solutions replicate the index with a much smaller tracking error than that of the ETFs considered.

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Section: Literature Reviewmentioning

confidence: 99%

Section: On the Distribution Of Returnsmentioning

confidence: 99%

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Forecasting portfolio returns with skew‐geometric Brownian motions

Bufalo

Liseo

Orlando

2022

Appl Stoch Models Bus & Ind

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“…In particular, it is interesting to know whether the fluctuations in many time series are really random or they are instead the product of a (complex) deterministic system [3][4][5][6]. The behavior of a completely random system is not predictable anyway.…”

Section: Introductionmentioning

confidence: 99%

Replication in Energy Markets: Use and Misuse of Chaos Tools

Mastroeni

Vellucci

2022

Entropy

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As pointed out by many researchers, replication plays a key role in the credibility of applied sciences and the confidence in all research findings. With regard, in particular, to energy finance and economics, replication papers are rare, probably because they are hampered by inaccessible data, but their aim is crucial. We consider two ways to avoid misleading results on the ostensible chaoticity of price series. The first one is represented by the proper mathematical definition of chaos and the related theoretical background, while the latter is represented by the hybrid approach that we propose here—i.e., consisting of considering the dynamical system underlying the price time series as a deterministic system with noise. We find that both chaotic and stochastic features coexist in the energy commodity markets, although the misuse of some tests in the established practice in the literature may say otherwise.

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“…The typical interchange between activity and calmer periods that we find in these systems is, in particular, found in biological neuronal activity. This is one of the reasons why in a recent work 6 , stock market indices developments were predicted by a deterministic low-dimensional neuroinformatics-borrowed Rulkov-type map 7 , and compared to the standard stochastic approach. This comparison yielded slightly superior modeling results of the deterministic over the stochastic one.…”

Section: Introductionmentioning

confidence: 99%

Exploiting deterministic features in apparently stochastic data

Stoop

Orlando

Bufalo

et al. 2022

Sci Rep

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Many processes in nature are the result of many coupled individual subsystems (like population dynamics or neurosystems). Not always such systems exhibit simple stable behaviors that in the past science has mostly focused on. Often, these systems are characterized by bursts of seemingly stochastic activity, interrupted by quieter periods. The hypothesis is that the presence of a strong deterministic ingredient is often obscured by the stochastic features. We test this by modeling classically stochastic considered real-world data from both, the stochastic as well as the deterministic approaches to find that the deterministic approach’s results level with those from the stochastic side. Moreover, the deterministic approach is shown to reveal the full dynamical systems landscape, which can be exploited for steering the dynamics into a desired regime.

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Financial markets’ deterministic aspects modeled by a low-dimensional equation

Cited by 17 publications

References 77 publications

Forecasting portfolio returns with skew‐geometric Brownian motions

Forecasting portfolio returns with skew‐geometric Brownian motions

Replication in Energy Markets: Use and Misuse of Chaos Tools

Exploiting deterministic features in apparently stochastic data

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