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25
Variation, jumps, market frictions and high frequency data in financial econometrics
, 2005
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Volatility Comovement: A Multifrequency Approach
, 2004
"... We implement a multifrequency volatility decomposition of three exchange rates and show that components with similar durations are strongly correlated across series. This motivates a bivariate extension of the MarkovSwitching Multifractal (MSM) introduced in Calvet and Fisher (2001, 2004). Bivariat ..."
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Cited by 15 (2 self)
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We implement a multifrequency volatility decomposition of three exchange rates and show that components with similar durations are strongly correlated across series. This motivates a bivariate extension of the MarkovSwitching Multifractal (MSM) introduced in Calvet and Fisher (2001, 2004). Bivariate MSM is a stochastic volatility model with a closedform likelihood. Estimation can proceed by ML for state spaces of moderate size, and by simulated likelihood via a particle filter in highdimensional cases. We estimate the model and confirm its main assumptions in likelihood ratio tests. Bivariate MSM compares favorably to a standard multivariate GARCH both in and outofsample. We extend the model to multivariate settings with a potentially large number of assets by proposing a parsimonious multifrequency factor structure.
Multifrequency JumpDiffusions: An Equilibrium Approach
, 2007
"... This paper proposes that equilibrium valuation is a powerful method to generate endogenous jumps in asset prices. We specify an economy with continuous consumption and dividend paths, in which endogenous price jumps originate from the market impact of regimeswitches in the drifts and volatilities ..."
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Cited by 5 (0 self)
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This paper proposes that equilibrium valuation is a powerful method to generate endogenous jumps in asset prices. We specify an economy with continuous consumption and dividend paths, in which endogenous price jumps originate from the market impact of regimeswitches in the drifts and volatilities of fundamentals. We parsimoniously incorporate regimes of heterogeneous durations and verify that the persistence of a shock endogenously increases the magnitude of the induced price jump. As the number of frequencies driving fundamentals goes to infinity, the price process converges to a novel stochastic process, which we call a multifractal jumpdiffusion.
Irregularities and scaling in signal and image processing: Multifractal analysis, to appear in
 M. Frame Ed., Benoit Mandelbrot: A Life in Many Dimensions, World Scientific
, 2012
"... B. Mandelbrot gave a new birth to the notions of scale invariance, selfsimilarity and noninteger dimensions, gathering them as the founding cornerstones used to build up fractal geometry. The first purpose of the present contribution is to review and relate together these key notions, explore thei ..."
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Cited by 3 (2 self)
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B. Mandelbrot gave a new birth to the notions of scale invariance, selfsimilarity and noninteger dimensions, gathering them as the founding cornerstones used to build up fractal geometry. The first purpose of the present contribution is to review and relate together these key notions, explore their interplay and show that they are different facets of a same intuition. Second, it will explain how these notions lead to the derivation of the mathematical tools underlying multifractal analysis. Third, it will reformulate these theoretical tools into a wavelet framework, hence enabling their better theoretical understanding as well as their efficient practical implementation. B. Mandelbrot used his concept of fractal geometry to analyze realworld applications of very different natures. As a tribute to his work, applications of various origins, and where multifractal analysis proved fruitful, are revisited to illustrate the theoretical developments proposed here.
Are European equity markets efficient? New evidence from fractal analysis
"... Abstract: Fractal analysis is carried out on the stock market indices of six developed European countries. Evidence is found of longrange autocorrelation in the log return series of the Mibtel, the index of the Italian stock market, in contravention of the Random Walk Hypothesis. Longrange autocor ..."
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Cited by 2 (0 self)
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Abstract: Fractal analysis is carried out on the stock market indices of six developed European countries. Evidence is found of longrange autocorrelation in the log return series of the Mibtel, the index of the Italian stock market, in contravention of the Random Walk Hypothesis. Longrange autocorrelation implies that predictable patterns in the log returns do not dissipate quickly, and may therefore produce potential arbitrage opportunities. No evidence contrary to the Random Walk Hypothesis is found for the other five stock markets.
Regimeswitching and the estimation of multifractal processes
 Journal of Financial Econometrics
, 2004
"... assistance was provided by Xifeng Diao. We are very appreciative of financial support provided ..."
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assistance was provided by Xifeng Diao. We are very appreciative of financial support provided
An Evolutionary Quantum Game Model of Financial Market Dynamics − Theory and Evidence Abstract
, 2007
"... The application of mathematical physics to economics has seen a recent development in the form of quantum game theory. Quantum game theory has become an important field of research in multidisciplinary applications of mathematical physics to the study of economic phenomena. We address the empirical ..."
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The application of mathematical physics to economics has seen a recent development in the form of quantum game theory. Quantum game theory has become an important field of research in multidisciplinary applications of mathematical physics to the study of economic phenomena. We address the empirical findings of multifractality and turbulence in financial markets ’ dynamics, from the point of view of evolutionary quantum game theory, proposing a quantum game theoretical model of a financial market, that extends the behavioral framework proposed by Sornette and Zhou for the selffulfulling Ising model of the markets. The quantum market model works with a bosonic framework for evolutionary quantum game theory introduced here and is based on recent findings within neuroeconomics and the neurobiology of decision. The model is tested against actual market data, where it is shown that it is able to reproduce some of the main multifractal signatures present in actual markets.
Higher Dimensional Multifractal Processes: Filtering via Simulation
, 2008
"... One important contribution has been made by Benoit Mandelbrot, the famous father of fractals who proposed a multifractal model of asset returns (MMAR), a theory which inherits all the hallmarks of Mandelbrot’s earlier work that has emerged since the 1970s. As a new formalization of stochastic model ..."
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One important contribution has been made by Benoit Mandelbrot, the famous father of fractals who proposed a multifractal model of asset returns (MMAR), a theory which inherits all the hallmarks of Mandelbrot’s earlier work that has emerged since the 1970s. As a new formalization of stochastic models for the volatility dynamics of asset prices, it preserves the hierarchical multiplicative structure of volatility components with different characteristic time scales, which are in harmony with the stylized facts of financial markets. In this paper, we concentrate on developing parsimonious multivariate multifractal processes, and implement their estimation via maximum likelihood approaches. We then apply our multivariate multifractal processes to empirically relevant topics, such as portfolio risk measurement and management.
“High Watermarks of Market Risks ” ♣
, 2007
"... The volatility has long been used as an auxiliary variable in the processes explaining the returns on risky assets. In this traditional framework, the observable were the returns and the volatility remained a latent variable, whose value or possible values were a byproduct of the estimation. Recent ..."
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The volatility has long been used as an auxiliary variable in the processes explaining the returns on risky assets. In this traditional framework, the observable were the returns and the volatility remained a latent variable, whose value or possible values were a byproduct of the estimation. Recently, the focus has changed and many studies have been devoted to empirical estimates of the volatility itself, without specifying necessarily any model for the prices themselves. This has been made possible by the increased availability of highfrequency data, and the theoretical works of BarndorffNielsen and Shephard (2002) showing convergence between an empirical measure of volatility and its theoretical expression. The empirical measure of volatility has been progressively refined, from a simple sum of squared returns to more sophisticated measures taking into account microstructure biases (see for instance Oomen, 2005). In parallel, some theoretical developments have put back into focus the role of jumps. There are now procedures to disentangle the jump part of the empirical volatility from its regular fluctuations. Taking the volatility as a random variable in itself means studying its characteristics. It is well known that volatility dynamics are autoregressive but also that obviously its process is stationary. Given that, it is natural to look for the best fit for the distribution of the volatility, given that the theory yields several possible candidates. Of special interest is the estimation of the likelihood of the volatility peaks, which relies on Extreme Value Theory. In this article, we first present several estimates of measures of risk, using both high frequency data and lower frequency data.
The Network for Mathematical Physics and Stochastics (MaPhySto),
"... Econometric analysis of realised covariation: high frequency based covariance, regression and correlation in financial economics ..."
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Econometric analysis of realised covariation: high frequency based covariance, regression and correlation in financial economics