Modeling stock prices by multifractional Brownian motion: an improved estimation of the pointwise regularity

Bianchi, Sergio; Pantanella, Alexandre; Pianese, Augusto

doi:10.1080/14697688.2011.594080

Cited by 72 publications

(58 citation statements)

References 34 publications

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“…Bianchi et al (see [14]) show that the assumption about K (which acts only on vertical shifts, as it is straightforward from Eq. (8)) is inessential because a procedure can be defined to estimate the true value of K. When the functional parameter is deterministic (following the above notation, when it is H(t)), q = 1 and H(t) = 1 2 , the estimator is normally distributed with mean equal to H(t), for any t, and variance equal to…”

Section: Moving Window Absolute Moment-based Estimatormentioning

confidence: 95%

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Efficient Markets and Behavioral Finance: A Comprehensive Multifractional Model

Bianchi

Pantanella

Pianese

2015

Advs. Complex Syst.

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Real-world financial dynamics daily do challenge the credibility of the Efficient Market Hypothesis, the pillar of the whole martingale-based modern financial theory stating that at any time asset prices discount all past information. As a matter of fact, the empirical evidence accumulated so far indicates that current models cannot explain the complexity of financial market movements, to the extent that a strand of skeptical thought, the Behavioral Finance, has been booming. The question whether a model exists which is able to make consistent the two paradigms is a living matter that financial markets demand to address. The paper deals with a parsimonious stochastic model able to include as special cases both market efficiency and "psychological" phenomena such as the underreaction and the overreaction, peculiar features of the behavioral finance. The great readability of the model, its capability to agree the controversial results provided by literature on efficient markets and the simplicity of the financial intuition it offers are discussed.

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Section: Moving Window Absolute Moment-based Estimatormentioning

confidence: 95%

“…Efficient Markets and Behavioral Finance: A Comprehensive Multifractional Model given by a (rescaled) B 0.3 (t) (for a justification of this simulation, see [14]). …”

Section: -10mentioning

confidence: 99%

Efficient Markets and Behavioral Finance: A Comprehensive Multifractional Model

Bianchi

Pantanella

Pianese

2015

Advs. Complex Syst.

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“…This phenomenon is called multiscaling and reflects the occurrence of different dynamics at different time-scales, it can be attributed to the heterogeneity of market participants. Time-dependent scaling behaviour has also been observed in financial time series [23,24], the local variations of roughness can be described by allowing the H exponent to vary with time [25].…”

Section: Introductionmentioning

confidence: 94%

Time-dependent scaling patterns in high frequency financial data

Nava

Matteo

Aste

2016

Eur. Phys. J. Spec. Top.

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Abstract. We measure the influence of different time-scales on the intraday dynamics of financial markets. This is obtained by decomposing financial time series into simple oscillations associated with distinct time-scales. We propose two new time-varying measures of complexity: 1) an amplitude scaling exponent and 2) an entropy-like measure. We apply these measures to intraday, 30-second sampled prices of various stock market indices. Our results reveal intraday trends where different time-horizons contribute with variable relative amplitudes over the course of the trading day. Our findings indicate that the time series we analysed have a non-stationary multifractal nature with predominantly persistent behaviour at the middle of the trading session and anti-persistent behaviour at the opening and at the closing of the session. We demonstrate that these patterns are statistically significant, robust, reproducible and characteristic of each stock market. We argue that any modelling, analytics or trading strategy must take into account these non-stationary intraday scaling patterns.

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“…Other approaches (e.g. Bianchi and Pianese [35] and Bianchi et al [36]) work appropriately with less data points, however, the methodology of these authors is parametric and imposes ex-ante limits on the shape of the parameter to be estimated.…”

Section: Introductionmentioning

confidence: 98%