A multifractal approach towards inference in finance
We introduce tools for inference in the multifractal random walk introduced by Bacry et al. (2001). These tools include formulas for smoothing, filtering and volatility forecasting. In addition, we present methods for computing conditional densities for one- and multi-step returns. The inference techniques presented in this paper, including maximum likelihood estimation, are applied to data from the Oslo Stock Exchange, and it is observed that the volatility forecasts based on the multifractal random walk have a much richer structure than the forecasts obtained from a basic stochastic volatility model.
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| Length: | |
| Date of creation: | Feb 2012 |
| Handle: | RePEc:arx:papers:1202.5376 |
| Contact details of provider: | Web page: http://arxiv.org/
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- Calvet, Laurent & Fisher, Adlai, 2001.
"Forecasting multifractal volatility,"
Journal of Econometrics,
Elsevier, vol. 105(1), pages 27-58, November.
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- Laurent Calvet & Adlai Fisher & Benoit Mandelbrot, 1999. "A Multifractal Model of Assets Returns," New York University, Leonard N. Stern School Finance Department Working Paper Seires 99-072, New York University, Leonard N. Stern School of Business-.
- Laurent-Emmanuel Calvet & Benoît B. Mandelbrot & Adlai J. Fisher, 2011. "A Multifractal Model of Asset Returns," Working Papers hal-00601870, HAL.
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- Thomas Lux, 2006. "The Markov-Switching Multifractal Model of Asset Returns: GMM Estimation and Linear Forecasting of Volatility," Working Papers wp06-19, Warwick Business School, Finance Group.
- Lux, Thomas, 2006. "The Markov-Switching Multifractal Model of asset returns: GMM estimation and linear forecasting of volatility," Economics Working Papers 2006,17, Christian-Albrechts-University of Kiel, Department of Economics.
- Benoit Mandelbrot, 2015. "The Variation of Certain Speculative Prices," World Scientific Book Chapters,in: THE WORLD SCIENTIFIC HANDBOOK OF FUTURES MARKETS, chapter 3, pages 39-78 World Scientific Publishing Co. Pte. Ltd..
- Benoit Mandelbrot, 1963. "The Variation of Certain Speculative Prices," The Journal of Business, University of Chicago Press, vol. 36, pages 394-394.
- Varadhan, Ravi & Gilbert, Paul, 2009. "BB: An R Package for Solving a Large System of Nonlinear Equations and for Optimizing a High-Dimensional Nonlinear Objective Function," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 32(i04).
- Sara Martino & Kjersti Aas & Ola Lindqvist & Linda Neef & Håvard Rue, 2011. "Estimating stochastic volatility models using integrated nested Laplace approximations," The European Journal of Finance, Taylor & Francis Journals, vol. 17(7), pages 487-503. Full references (including those not matched with items on IDEAS)
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