Modelling fluctuations of financial time series: from cascade process to stochastic volatility model

By Jean-François Muzy, J. Delour, E. France, Cmap Ecole Polytecnhique Palaiseau France. 2000

294 citations recorded by the source corpus.

Abstract:In this paper, we provide a simple, “generic” interpretation of multifractal scaling laws and multiplicative cascade process paradigms in terms of volatility correlations. We show that in this context 1/f power spectra, as recently observed in reference [23], naturally emerge. We then propose a simple solvable “stochastic volatility” model for return fluctuations. This model is able to reproduce most of recent empirical findings concerning financial time series: no correlation between price variations, long-range volatility correlations and multifractal statistics. Moreover, its extension to a multivariate context, in order to model portfolio behavior, is very natural. Comparisons to real data and other models proposed elsewhere are provided.

Subfields: Condensed Matter Physics, Economics and Econometrics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/6672fc266e03261f453eec60b84efd58cb7a933b

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Citations in the corpus

Testing the Gaussian copula hypothesis for financial assets dependences (2001, unknown): “risks, and by Rosenberg (1999) or Cherubini and Luciano”
A multifractal approach for stock market inefficiency (2008, background): “Moreover, multifractal theoretical models were introduced [17–24] that take into account important aspects of price patterns (stylized facts), that other traditional models such as fractional Brownian motion and GARCH processes cannot.”
Multi-scaling in finance (2007, background): “…pertinent (Ghashghaie et al. 1996, Calvet and Fisher 2002) and there are several multi-scaling models proposed in the literature (Ding et al. 1993, Muzy et al. 1994, 2000, Ghashghaie et al. 1996, Mandelbrot et al. 1997, Arneodo et al. 1998, Mandelbrot 1999, Bacry et al. 2001, Calvet and Fisher…”
On non-Gaussianity and dependence in financial time series: a nonextensive approach (2005, background): “2000 ) present an analytical connection with entropic index q , i.”
Random walks, liquidity molasses and critical response in financial markets (2004, background): “…KOCKELKOREN and MARC POTTERS Science & Finance, Capital Fund Management, 6–8 Bvd Haussmann, 75009 Paris, France (Received 11 June 2004; in final form 3 October 2005) Stock prices are observed to be random walks in time despite a strong, long-term memory in the signs of trades (buys or sells).”
Fluctuations and response in financial markets: the subtle nature of ‘random’ price changes (2003, unknown): “For reasons that we explain in more details below, liquidity providers act such as to create anti-persistence (or mean reversion) in price changes that lead to a sub-diffusive behaviour of the price, whereas liquidity takers’ action leads to persistence and super-diffusive behaviour.”
The Joint Distribution of Stock Returns is Not Elliptical (2010, unknown): “If we now choose σ = σ0e ξ with ξ ∼ N (0, s) (as suggested by advocates of multifractal models [3,28,35]), the resulting multivariate model defines the log-normal ensemble and the log-normal copula.”
Empirical properties of asset returns: stylized facts and statistical issues (2001, methodology): “Recent work [90,100] on multifractal stochastic volatility models has motivated yet another measure of nonlinear dependence based on correlations of the logarithm of absolute returns:”
Large Stock Market Price Drawdowns Are Outliers (2000, unknown): “2¶ ¶ ¸¥º À¥O« º;§ ¯Ç¶ ©NO« ¾³¥É=¾¿ § ºUÉ9© § «[¶¹¬=¬e§ « ¾³O©N§¹Ì=¶ ¸¥¾¿OÉe¯;Ñz© k«{§ ºUÈeº;©N± ÉeºU¥º;§ ©N± ´²¬N§ µj¯;Ê0ú¥¬e§aª®¸¥¬ÂºUÈeºU§ Æ9O¬cªo¯¼¶ ¸¥º ª'©VÌÂ¯¨¬ ´'ò¼© ¶¹À¥§ ºjª®¾¿±³±Bµj¬N§ º ºL©N¯¹¾¿±³Ì[¥¬N¶¹¾Å» ºj¸¥ºU§ «¥ºUÈÂ¾³© ¶¹¾³¬NO¯;ûz©NO« Ñ ¬e ¶ ¸¥ºj¬ ¶ ¸¥ºU§a¸O©NO« Ñ ª®¸O¬9º;ÈNº;§ ÆÂ¥¬c”
Stock price jumps: news and volume play a minor role (2008, background): “Many of these properties look very similar to endogenous noise generated by complex, non-linear systems with feedback, such as turbulent flows [5, 6, 7, 8, 9], stick balancing dynamics [10], etc.”