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Quantitative Finance Volume 13, 2013 - Issue 8: Themed Issue on Derivatives
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Research Papers

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

S. Bianchi Istituzioni Metodi Quantitativi e Territorio, University of Cassino, Via S. Angelo loc. Folcara, Cassino, 03043, ItalyCorrespondence[email protected]
,
A. Pantanella Istituzioni Metodi Quantitativi e Territorio, University of Cassino, Via S. Angelo loc. Folcara, Cassino, 03043, Italy
&
A. Pianese Istituzioni Metodi Quantitativi e Territorio, University of Cassino, Via S. Angelo loc. Folcara, Cassino, 03043, Italy
Pages 1317-1330 | Received 21 Jul 2010, Accepted 01 Jun 2011, Published online: 26 Aug 2011

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Fabian A. Harang, Torstein K. Nilssen & Frank N. Proske. (2022) Girsanov theorem for multifractional Brownian processes. Stochastics 94:8, pages 1137-1165.
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J. Lévy Véhel, A. Philippe & C. Robet. (2021) Explicit and combined estimators for parameters of stable distributions. Statistics 55:4, pages 736-764.
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Mark Hallam & Jose Olmo. (2018) Statistical tests of distributional scaling properties for financial return series. Quantitative Finance 18:7, pages 1211-1232.
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Antoine Ayache & Julien Hamonier. (2017) Behaviour of linear multifractional stable motion: membership of a critical Hölder space. Stochastics 89:5, pages 709-725.
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Daniele Angelini & Sergio Bianchi. (2023) Nonlinear biases in the roughness of a Fractional Stochastic Regularity Model. Chaos, Solitons & Fractals 172, pages 113550.
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Massimiliano Frezza, Sergio Bianchi & Augusto Pianese. (2023) Nonlinearity of the volume–volatility correlation filtered through the pointwise Hurst–Hölder regularity. Communications in Nonlinear Science and Numerical Simulation 121, pages 107204.
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Sergio Bianchi, Massimiliano Frezza, Augusto Pianese & Anna Maria Palazzo. 2022. Mathematical and Statistical Methods for Actuarial Sciences and Finance. Mathematical and Statistical Methods for Actuarial Sciences and Finance 96 102 .
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Fabian A. Harang, Marc Lagunas-Merino & Salvador Ortiz-Latorre. (2021) Self-exciting multifractional processes. Journal of Applied Probability 58:1, pages 22-41.
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Raffaele Mattera & Fabrizio Di Sciorio. (2020) Option Pricing Under Multifractional Process and Long-Range Dependence. Fluctuation and Noise Letters 20:01, pages 2150008.
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Massimiliano Frezza, Sergio Bianchi & Augusto Pianese. (2021) Fractal analysis of market (in)efficiency during the COVID-19. Finance Research Letters 38, pages 101851.
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Sergio Bianchi, Augusto Pianese, Massimiliano Frezza & Anna Maria Palazzo. 2021. Mathematical and Statistical Methods for Actuarial Sciences and Finance. Mathematical and Statistical Methods for Actuarial Sciences and Finance 95 101 .
Michał Balcerek & Krzysztof Burnecki. (2020) Testing of Multifractional Brownian Motion. Entropy 22:12, pages 1403.
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Sergio Bianchi, Augusto Pianese & Massimiliano Frezza. (2020) A distribution‐based method to gauge market liquidity through scale invariance between investment horizons. Applied Stochastic Models in Business and Industry 36:5, pages 809-824.
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Rosella Castellano, Roy Cerqueti & Giulia Rotundo. (2018) Exploring the financial risk of a temperature index: a fractional integrated approach. Annals of Operations Research 284:1, pages 225-242.
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Qidi Peng & Ran Zhao. (2018) A general class of multifractional processes and stock price informativeness. Chaos, Solitons & Fractals 115, pages 248-267.
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Massimiliano Frezza. (2018) A fractal-based approach for modeling stock price variations. Chaos: An Interdisciplinary Journal of Nonlinear Science 28:9.
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Pierre Raphaël Bertrand, Jean-Louis Combes, Marie-Eliette Dury & Doha Hadouni. (2018) Overfitting of Hurst estimators for multifractional Brownian motion: A fitting test advocating simple models. Risk and Decision Analysis 7:1-2, pages 31-49.
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Antoine Ayache, Céline Esser & Julien Hamonier. (2018) A new multifractional process with random exponent. Risk and Decision Analysis 7:1-2, pages 5-29.
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Sergio Bianchi & Augusto Pianese. (2018) Time-varying Hurst–Hölder exponents and the dynamics of (in)efficiency in stock markets. Chaos, Solitons & Fractals 109, pages 64-75.
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Sixian Jin, Qidi Peng & Henry Schellhorn. (2016) Estimation of the pointwise Hölder exponent of hidden multifractional Brownian motion using wavelet coefficients. Statistical Inference for Stochastic Processes 21:1, pages 113-140.
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Augusto Pianese, Sergio Bianchi & Anna Maria Palazzo. (2018) Fast and unbiased estimator of the time-dependent Hurst exponent. Chaos: An Interdisciplinary Journal of Nonlinear Science 28:3.
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Yi-Cheng Tsai, Chin-Laung Lei, William Cheung, Chung-Shu Wu, Jan-Ming Ho & Chuan-Ju Wang. (2018) Exploring the Persistent Behavior of Financial Markets. Finance Research Letters 24, pages 199-220.
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Britta Förster & Bernd Hayo. (2018) Monetary and Fiscal Policy in Times of Crisis: A New Keynesian Perspective in Continuous Time. The Manchester School 86:1, pages 21-48.
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Sergio Bianchi & Massimiliano Frezza. (2017) Fractal stock markets: International evidence of dynamical (in)efficiency. Chaos: An Interdisciplinary Journal of Nonlinear Science 27:7.
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Antoine Ayache & Julien Hamonier. (2017) Uniformly and strongly consistent estimation for the Hurst function of a Linear Multifractional Stable Motion. Bernoulli 23:2.
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Noemi Nava, Tiziana Di Matteo & Tomaso Aste. (2016) Time-dependent scaling patterns in high frequency financial data. The European Physical Journal Special Topics 225:10, pages 1997-2016.
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H.S. Zhang, X.Y. Shen & J.P. Huang. (2016) Pattern of trends in stock markets as revealed by the renormalization method. Physica A: Statistical Mechanics and its Applications 456, pages 340-346.
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Nikolas Gerlich & Stefan Rostek. (2015) Estimating serial correlation and self-similarity in financial time series—A diversification approach with applications to high frequency data. Physica A: Statistical Mechanics and its Applications 434, pages 84-98.
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Roy Cerqueti & Giulia Rotundo. (2014) A review of aggregation techniques for agent-based models: understanding the presence of long-term memory. Quality & Quantity 49:4, pages 1693-1717.
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Kęstutis Kubilius, Yuliya Mishura, Kostiantyn Ralchenko & Oleg Seleznjev. (2015) Consistency of the drift parameter estimator for the discretized fractional Ornstein–Uhlenbeck process with Hurst index $H\in(0,\frac{1}{2})$. Electronic Journal of Statistics 9:2.
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Sergio Bianchi & Augusto Pianese. 2015. Future Perspectives in Risk Models and Finance. Future Perspectives in Risk Models and Finance 247 285 .
Massimiliano Frezza. (2014) Goodness of fit assessment for a fractal model of stock markets. Chaos, Solitons & Fractals 66, pages 41-50.
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Meng Li, Xiaofeng Hui, Misao Endo & Kazuo Kishimoto. (2014) A quantitative model for intraday stock price changes based on order flows. Journal of Systems Science and Complexity 27:1, pages 208-224.
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Jungjun Park. (2020) Estimating the DJI Series by Multifractional Brownian Motion. SSRN Electronic Journal.
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Yanyan Yang & Qidi Peng. (2017) Do Sentiment and Exchange Rate Share Memories? An Application of Multifractional Process Modeling. SSRN Electronic Journal.
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Bernd Hayo & Britta Niehof. (2014) Monetary and Fiscal Policy in Times of Crises: A New Keynesian Perspective in Continuous Time. SSRN Electronic Journal.
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Stefan Rostek. (2014) More than You Ever Wanted to Know About the VIX: Bringing Together Serial Correlation and Volatility Clustering. SSRN Electronic Journal.
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Sergio Bianchi & Augusto Pianese. (2013) Multifractional Processes in Finance. SSRN Electronic Journal.
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Sergio Bianchi, Alexandre Pantanella & Augusto Pianese. (2012) Local Estimation of Stock Market Efficiency. SSRN Electronic Journal.
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