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Multifractal Volatility: Theory, Forecasting, and Pricing (Academic Press Advanced Finance), by Laurent E. Calvet, Adlai J. Fisher
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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 their book 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.
· 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
- Sales Rank: #1575974 in Books
- Published on: 2008-09-16
- Original language: English
- Number of items: 1
- Dimensions: 9.02" h x .63" w x 5.98" l, 1.25 pounds
- Binding: Hardcover
- 272 pages
Review
Advance Praise for Multifractal Volitility
“I thoroughly enjoyed reading the book and highly recommend it. The authors masterfully present their work on the Markov-Switching Multifractal model and its implications for Asset Pricing. This is a wonderful contribution to the field of Financial Economics.”
-Ravi Bansal, J.B. Fuqua Professor of Finance, Duke University Durham, NC
“I have always been intrigued by the multi-fractal approach to volatility modeling, forecasting and pricing pioneered by Calvet and Fisher. This book does a wonderful job in gathering together all of the fundamental ideas and results in a coherent framework, and I highly recommend it to anybody interested in learning more about these novel techniques and how they compare to the more traditional GARCH and stochastic volatility based modeling procedures.”
-Tim Bollerslev, Juanita and Clifton Kreps Professor of Economics, Duke University, NC
“This starkly original work defines a key part of the research frontier, developing a ‘multifractal’ perspective on volatility that unifies regime-switching and long memory, in discrete and continuous time, univariate and multivariate. Simultaneously and astonishingly, it is of immediate practical relevance for asset management, asset pricing and risk management. This book is required reading, for academics and practitioners alike.”
-Francis X. Diebold, J.M. Cohen Professor of Economics, University of Pennsylvania
"Calvet and Fisher have fashioned the definitive treatment of multi-fractal models of return volatility. Since Mandelbrot first challenged the standard paradigm, evidence supporting the parsiomony and flexibility of the multifractal approach has accumulated. Calvet and Fisher are uniquely positioned to finally unify this progress, much of which is based on their own research. The result is masterful and convincing, particularly for capturing return risk over multiple time horizons. I highly recommend their book."
-Darrell Duffie, Dean Witter Distinguished Professor of Finance, Stanford University, CA
“This book offers a unified treatment of multifractal volatility, a remarkable approach developed by the authors in a series of earlier papers. The idea is to capture in a single, coherent framework the set of observed features of financial data, whether seen as “jumps” in continuous-time models, “fat tails” in data discretely sampled over short intervals, different characterizations of volatility persistence over intermediate and long horizons, and nonlinearities and skewness in the conditional distributions. The underlying framework is a Markov-switching model with a very large number of different regimes, with the nature of different regimes summarized by a much smaller set of parameters. The book provides an excellent illustration of just how successful this flexible yet parsimonious approach can be in terms of describing a wide variety of the characteristics of financial time series.”
-James Hamilton, Professor of Economics, University of California, San Diego
“Calvet and Fisher provide a valuable and thorough development of a novel class of models of financial market volatility. The methods and models exposited so nicely in their book should be part of the toolkit of researchers interested in understanding and characterizing the stochastic nature of volatility fluctuations. Their book is simultaneously accessible and complete. It shows how to use these models in practice, and it provides a rigorous foundation for their application.”
-Lars Hansen, Livingston Distinguished Service Professor, University of Chicago, IL
“Volatility is a central concern of modern financial econometrics, challenging econometricians to build plausible models and practical methods of inference. Calvet and Fisher draw together the ingredients of a promising new research agenda, integrating a decade of work on multifractal modeling into a masterful overview of the field of volatility, demonstrating the advantages of Markov switching multifractals in aggregating components of differing persistence and showing us how rare events need not be studied in isolation as curiosa. A compelling read for financial theorists and practitioners.”
-Peter C. B. Philips, Sterling Professor of Economics & Statistics, Yale University, CT
“To accommodate the high persistence and variability of volatility in financial time series, Calvet and Fisher developed the class of Markov-Switching Multifractal models. This book, which summarizes ten years of their research, is of great interest to researchers in asset pricing and essential reading for practitioners working on risk management or volatility forecasting.”
-Jose Scheinkman, Theodore Wells '29 Professor of Economics, Princeton University, NJ
From the Back Cover
Advance Praise for Multifractal Volitility
“I thoroughly enjoyed reading the book and highly recommend it. The authors masterfully present their work on the Markov-Switching Multifractal model and its implications for Asset Pricing. This is a wonderful contribution to the field of Financial Economics.”
-Ravi Bansal, J.B. Fuqua Professor of Finance, Duke University Durham, NC
“I have always been intrigued by the multi-fractal approach to volatility modeling, forecasting and pricing pioneered by Calvet and Fisher. This book does a wonderful job in gathering together all of the fundamental ideas and results in a coherent framework, and I highly recommend it to anybody interested in learning more about these novel techniques and how they compare to the more traditional GARCH and stochastic volatility based modeling procedures.”
-Tim Bollerslev, Juanita and Clifton Kreps Professor of Economics, Duke University, NC
“This starkly original work defines a key part of the research frontier, developing a ‘multifractal’ perspective on volatility that unifies regime-switching and long memory, in discrete and continuous time, univariate and multivariate. Simultaneously and astonishingly, it is of immediate practical relevance for asset management, asset pricing and risk management. This book is required reading, for academics and practitioners alike.”
-Francis X. Diebold, J.M. Cohen Professor of Economics, University of Pennsylvania
"Calvet and Fisher have fashioned the definitive treatment of multi-fractal models of return volatility. Since Mandelbrot first challenged the standard paradigm, evidence supporting the parsiomony and flexibility of the multifractal approach has accumulated. Calvet and Fisher are uniquely positioned to finally unify this progress, much of which is based on their own research. The result is masterful and convincing, particularly for capturing return risk over multiple time horizons. I highly recommend their book."
-Darrell Duffie, Dean Witter Distinguished Professor of Finance, Stanford University, CA
“This book offers a unified treatment of multifractal volatility, a remarkable approach developed by the authors in a series of earlier papers. The idea is to capture in a single, coherent framework the set of observed features of financial data, whether seen as “jumps” in continuous-time models, “fat tails” in data discretely sampled over short intervals, different characterizations of volatility persistence over intermediate and long horizons, and nonlinearities and skewness in the conditional distributions. The underlying framework is a Markov-switching model with a very large number of different regimes, with the nature of different regimes summarized by a much smaller set of parameters. The book provides an excellent illustration of just how successful this flexible yet parsimonious approach can be in terms of describing a wide variety of the characteristics of financial time series.”
-James Hamilton, Professor of Economics, University of California, San Diego
“Calvet and Fisher provide a valuable and thorough development of a novel class of models of financial market volatility. The methods and models exposited so nicely in their book should be part of the toolkit of researchers interested in understanding and characterizing the stochastic nature of volatility fluctuations. Their book is simultaneously accessible and complete. It shows how to use these models in practice, and it provides a rigorous foundation for their application.”
-Lars Hansen, Livingston Distinguished Service Professor, University of Chicago, IL
“Volatility is a central concern of modern financial econometrics, challenging econometricians to build plausible models and practical methods of inference. Calvet and Fisher draw together the ingredients of a promising new research agenda, integrating a decade of work on multifractal modeling into a masterful overview of the field of volatility, demonstrating the advantages of Markov switching multifractals in aggregating components of differing persistence and showing us how rare events need not be studied in isolation as curiosa. A compelling read for financial theorists and practitioners.”
-Peter C. B. Philips, Sterling Professor of Economics & Statistics, Yale University, CT
“To accommodate the high persistence and variability of volatility in financial time series, Calvet and Fisher developed the class of Markov-Switching Multifractal models. This book, which summarizes ten years of their research, is of great interest to researchers in asset pricing and essential reading for practitioners working on risk management or volatility forecasting.”
-Jose Scheinkman, Theodore Wells '29 Professor of Economics, Princeton University, NJ
About the Author
By Laurent E. Calvet and Adlai J. Fisher
Most helpful customer reviews
15 of 15 people found the following review helpful.
Great source on state-of-the-art volatility modeling in Finance
By N. Tuzov
This book reflects a significant step in volatility modeling with a clear focus on financial applications. It offers a nice combination of theoretical results combined with fitting the corresponding models to real financial data.
From a practical point of view, it has been long known that (log) asset prices are not adequately described by Brownian Motion (BM) or Fractional BM. For instance, take the fact that typically, low-frequency (weekly or monthly) return distribution has much thinner tails than high-frequency (daily or hourly) return distribution. Such absence of "self-similarity" across frequencies is not consistent with BM or Fractional BM.
To capture this effect (among many others), they propose to model the (log) asset price as a Multifractal Process. Such process is characterized by so-called "scaling function" which can be estimated from the data. One may think of Multifractal Processes as an extended class of stochastic processes that includes self-similar BM / Fractional BM. In particular, for self-similar processes the scaling function has to be linear. However, estimations based on real currency and equity data (see Chapter 8) do not produce a linear scaling function. Therefore, the hypothesis of self-similarity (also called "unifractality") of the (log) asset price doesn't hold.
Apparently, the limitations of self-similar processes have been known for a while, and many popular volatility models (such as GARCH or FIGARCH) address them to a certain degree. However, numerical results show that the Multifractal Model is a better fit to the data in terms of scaling function.
In practice, the multifractal approach is implemented as so-called Markov-Switching Multifractal model (MSM) in discrete time. Markov-Switching models (pioneered by Hamilton, see Time Series Analysis) are based on the idea is that volatility (and possibly drift) are dependent on the unobserved state variable that follows a Markov process. MSM extends that idea by imposing certain restrictions on the transition matrix, thus reducing the dimensionality. The physical meaning of the restrictions is that different economic factors (technology shocks, business cycles, liquidity shocks) affect the volatility on different time scales. The volatility impact from one economic factor can be a lot more lasting than that from another factor.
The authors demonstrate that MSM model accounts for such data features as:
1) short- and long-range dependence in volatility;
2) fat tails of return distribution;
3) volatility jumps.
Again, many previously known models account for these effects to a certain extent, so a comparison to some benchmark models is necessary. Fitting MSM model to daily currency data via Maximum Likelihood (Chapter 3) shows that MSM is superior to:
1) GARCH-t ("t" means that the error term has a t-distribution)
2) Markov-Switching GARCH-t
3) FIGARCH-t
Personally, I would have liked to see how well MSM competes with some models based on Extreme Value Distribution, but no examples are provided.
There have been many complaints in the reviews of the popular book of Mandelbrot (see The Misbehavior of Markets: A Fractal View of Financial Turbulence) that few "implementation details" had been provided. Numerical examples in Calvet and Fisher clearly show how to apply Mandelbrot's ideas to real data and where exactly the new framework surpasses the existing volatility models.
Other chapters include multivariate volatility modeling (again, MSM is superior to multivariate CC-GARCH) and application of MSM to asset pricing theory. Therefore, I can highly recommend this book to people interested in the latest advances in volatility modeling.
11 of 11 people found the following review helpful.
An excellent review of an important topic
By Aaron C. Brown
With all due respect to the other reviewers, there's not much point discussing how good a job this book does explaining multifractal volatility. It's the only book on that subject. I think it's more useful to describe why someone who doesn't already know what MV is might want to read this excellent book.
A lot of financial data series (and non-financial as well) exhibit apparently erratic behavior such as sudden jumps or periods of high and low volatility. These have caused many disasters, but also present tempting opportunity for anyone who can understand them. The tricky part is that simple models don't provide good fits, and complicated models are too hard to calibrate.
There are some standard approaches to this problem and the authors have come up with one they think is better. But you don't need to accept that to find this book useful. It lays out a general mathematical framework and covers a wide range of models, comparing them both mathematically and with financial data. The mathematics is only moderately difficult, and the clear presentation explains the main ideas for people who cannot follow each step of the formalism. Whether or not you like MV, and it is a small group so far that does, this book is the best up-to-date introduction to this field. There are extensive references to a wide range of approaches. The material is presented as a set of tools and ideas, you can take the ones you find useful and combine them as you like.
It would be even better if the book included data and computer code, either on a CD or at a website. More discussion of data would be helpful, as would some applications that go beyond data fitting (for example, it would be nice to see MV make money, or warn of disasters). The charts and tables are ugly, and the charts absurdly small for the information they are intended to convey. Some of the chapters could have used better editing to smooth over their origins as journal articles.
However, those are minor criticisms compared to the outstanding job the authors have done of summarizing important work in time series modeling, with rigor and depth, but without making the work inaccessible to a wide audience.
9 of 10 people found the following review helpful.
time scale sensitive discussion of a new volatiltiy theory
By Bachelier
Calvet & Fisher's "Multifractal Volatility: Theory, Forecasting, and Pricing" is a welcome addition to the conversation in mathematical finance on volatility modeling expectations and tractable and practical models.
Multifractal Volatility (MV) covers novel techniques outside of more traditional GARCH and stochastic volatility models (the controlling state variable is unobserved), and builds on the thinking of Benoit Mandelbrot on a sub-set of mathematics known as fractals, which are systems of non-linear equations that exhibit such characteristics as self-similarity (linear, non-linear, or statistical), scale invariance, and a (usually) non-integer Hausdorff dimension. Capturing fractals over multiple time horizons is the game.
(Note: there is a tedious back-and-forth about how Mandelbrot fractals are nothing but Elliott wave principal dressed up as higher mathematics. If your idea of fun is reading about cranks snarking at each other, G--gle it all up and have fun reading).
MV holds that both market returns and volatility exhibit strong kurtosis in the distribution of measured outcomes (i.e. there is a strong and sticky tendency for returns to stay either very close to the mean or far from it).
MV addresses the curse of dimensionality of regime switching state models (because the number of parameters increases with the square of the number of states) buy using a Markov-Switching Multifractal (MSM) model, where volatility is assumed to be drawn from a large discrete distribution, each of which can randomly switch to a new value drawn from a common distribution. The variable order is along regime switching probability, and increases smoothly for low to high frequency observations, but allows volatility major jumps when a regime switch occurs.
The first section introduces MSM in discrete time, followed by a section extending (or restating) the model in Continuous Time, followed by an examination of information arrival and Equilibrium Pricing.
This work is for specialists and persons well-trained in mathematical finance who are familiar with date measure and distributions. It assumes knowledge of Brownian Motion, Markov chains, equilibrium pricing, information theory, and regime switching (knowledge from fluid mechanics on viscosity would also help). It introduces and argues for fractal distributions of volatility for higher goodness of fit, and makes a strong case.
MV is well-written and clear, and even those who are not familiar or highly trained in the intricacies of Mandelbrot sets and other fractals can comprehend the arguments Calvet and Fisher make. This is a curious and interesting book and deserves a front-row seat in the continuing conversation in mathematical finance.
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