Multifractal Volatility

Multifractal Volatility

Theory, Forecasting, and Pricing

1st Edition - September 2, 2008

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  • Authors: Laurent Calvet, Adlai Fisher
  • eBook ISBN: 9780080559964
  • Hardcover ISBN: 9780121500139

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Calvet and Fisher present a powerful, new technique for volatility forecasting that draws on insights from the use of multifractals in the natural sciences and mathematics and provides a unified treatment of the use of multifractal techniques in finance. A large existing literature (e.g., Engle, 1982; Rossi, 1995) models volatility as an average of past shocks, possibly with a noise component. This approach often has difficulty capturing sharp discontinuities and large changes in financial volatility. Their research has shown the advantages of modelling volatility as subject to abrupt regime changes of heterogeneous durations. Using the intuition that some economic phenomena are long-lasting while others are more transient, they permit regimes to have varying degrees of persistence. By drawing on insights from the use of multifractals in the natural sciences and mathematics, they show how to construct high-dimensional regime-switching models that are easy to estimate, and substantially outperform some of the best traditional forecasting models such as GARCH. The goal of Multifractal Volatility is to popularize the approach by presenting these exciting new developments to a wider audience. They emphasize both theoretical and empirical applications, beginning with a style that is easily accessible and intuitive in early chapters, and extending to the most rigorous continuous-time and equilibrium pricing formulations in final chapters.

Key Features

  • Presents a powerful new technique for forecasting volatility
  • Leads the reader intuitively from existing volatility techniques to the frontier of research in this field by top scholars at major universities
  • The first comprehensive book on multifractal techniques in finance, a cutting-edge field of research


Finance practitioners, academics, and students, and econometriciansSecondary readership: Mathematicians, statisticians, and natural scientists interested in fractals

Table of Contents

  • Contents
    Chapter 1 Introduction
    Chapter 2 Background
    2.1 Autoregressive Volatility Modeling
    2.2 Multifractals in the Natural Sciences
    Chapter 3 The Multifractal Volatility Model: The MMAR
    3.1 The Multifractal Model of Asset Returns
    3.2 An Extension with Autocorrelated Returns
    3.3 Empirical Evidence
    3.4 Discussion
    Chapter 4 The Marko-Switching Multifractal (MSM) in Discrete Time
    4.1 MSM Construction in Discrete Time
    4.2 Maximum Likelihood Estimation
    4.3 Empirical Results
    4.4 Comparison with Alternative Models
    4.5 Discussion
    Chapter 5. Multivariate MSM
    5.1 Comovement of Univariate Volatility Components
    5.2 A Bivariate Multifrequency Model
    5.3 Inference
    5.4 Empirical Results
    5.5 Extension to Many Assets
    5.6 Discussion
    Chapter 6 The Marko-Switching Multifractal in Continuous Time
    6.1 MSM in Continuous - Time
    6.2 The Financial Model
    6.3 Forecasting the Distribution of Returns
    6.4 Discussion
    Chapter 7 Multifrequency News and Stock Returns
    7.1 An asset pricing model with regime-switching dividents
    7.2 Volatility feedback with multifrequency shocks
    7.3 Empirical results with fully informaed investros
    7.4 Learning about volatility and endogenous skewness
    7.5 Robustness checks, preference implications, and extension
    7.6 Discussion
    Chapter 8 Multifrequency Jump Diffusions
    8.1 An Equilibrium Model with Endogenous Price Jumps
    8.2 A Multifrequency Jump-Difussion for Equilibrium Stock Prices
    8.3 Price Dynamics with an Infinity of Frequencies
    8.4 Recursive Utility and Priced Jumps
    8.5 Discussion
    Chapter 9 Conclusion

Product details

  • No. of pages: 272
  • Language: English
  • Copyright: © Academic Press 2008
  • Published: September 2, 2008
  • Imprint: Academic Press
  • eBook ISBN: 9780080559964
  • Hardcover ISBN: 9780121500139

About the Authors

Laurent Calvet

Affiliations and Expertise

Professor, Chair in Finance - Tanaka Business School, Imperial College London, UK

Adlai Fisher

Affiliations and Expertise

Faculty of Commerce, University of British Columbia, Vancouver, Canada

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