## Volatility clustering in financial markets: Empirical facts and agent based models (2004)

### Cached

### Download Links

Citations: | 12 - 0 self |

### BibTeX

@TECHREPORT{Cont04volatilityclustering,

author = {Rama Cont},

title = {Volatility clustering in financial markets: Empirical facts and agent based models},

institution = {},

year = {2004}

}

### OpenURL

### Abstract

Summary. Time series of financial asset returns often exhibit the volatility clustering property: large changes in prices tend to cluster together, resulting in persistence of the amplitudes of price changes. After recalling various methods for quantifying and modeling this phenomenon, we discuss several economic mechanisms which have been proposed to explain the origin of this volatility clustering in terms of behavior of market participants and the news arrival process. A common feature of these models seems to be a switching between low and high activity regimes with heavytailed durations of regimes. Finally, we discuss a simple agent-based model which links such variations in market activity to threshold behavior of market participants and suggests a link between volatility clustering and investor inertia. 1

### Citations

718 |
Statistics for Long-Memory Processes
- Beran
- 1994
(Show Context)
Citation Context ...hin one of the two categories. The long range dependence property (3) hinges upon the behavior of the autocorrelation function at large lags, a quantity which may be difficult to estimate empirically =-=[7]-=-. For this reason, models with long-range dependence are often formulated in terms of self-similar processes, which allow to extrapolate across time scales and deduce long time behavior from short tim... |

531 |
Fractional Brownian motions, fractional noises and applications
- MANDELBROT, NESS
- 1968
(Show Context)
Citation Context ...ocess, but eventually for its increments (if they are stationary). The typical example of self-similar processs6 Rama Cont whose increments exhibit long range dependence is fractional Brownian motion =-=[43]-=-. But self-similarity does not imply long-range dependence in any way: αstable Lévy processes provide examples of self-similar processes with independent increments. Nor is self-similarity implied by ... |

352 | A Long Memory Property of Stock Market Returns and a New Model
- Ding, Granger, et al.
- 1993
(Show Context)
Citation Context ...oduction The study of statistical properties of financial time series has revealed a wealth of interesting stylized facts which seem to be common to a wide variety of markets, instruments and periods =-=[12, 16, 25, 47]-=-: • Excess volatility: many empirical studies point out to the fact that it is difficult to justify the observed level of variability in asset returns by variations in “fundamental” economic variables... |

293 |
Indirect inference
- Gouriéroux, Monfort, et al.
- 1993
(Show Context)
Citation Context ...ut pinpointing a specific stochastic model by testing for similar behavior of sample autocorrelations in agent-based models (described below), and using sample autocorrelations for indirect inference =-=[22]-=- of the parameters of such models.s8 Rama Cont 3 Mechanisms for volatility clustering While GARCH, FIGARCH and stochastic volatility models propose statistical constructions which mimick volatility cl... |

265 | Non-Gaussian Ornstein-Uhlenbeck-based models and some of their uses in financial economics
- Barndorff-Nielsen, Shephard
(Show Context)
Citation Context ...ets 7 in signs [26]. Many authors have thus suggested models, such as FIGARCH [4], in which returns have no autocorrelation but their amplitudes have long range dependence [4, 18]. It has been argued =-=[33, 5]-=- that the decay of C |r|(τ) can also be reproduced by a superposition of several exponentials, indicating that the dependence is characterized by multiple time scales. In fact, an operational definiti... |

223 |
Long memory processes and fractional integration in econometrics
- Baillie
- 1996
(Show Context)
Citation Context ...when |rt| verifies (3). Asset returns do not seem to possess long range dependencesVolatility Clustering in Financial Markets 7 in signs [26]. Many authors have thus suggested models, such as FIGARCH =-=[4]-=-, in which returns have no autocorrelation but their amplitudes have long range dependence [4, 18]. It has been argued [33, 5] that the decay of C |r|(τ) can also be reproduced by a superposition of s... |

214 | Long memory relationships and aggregation of dynamic models
- Granger
- 1980
(Show Context)
Citation Context ...n considered as a possible origin for various stylized facts [25]. Long term investors naturally focus on long-term behavior of prices, whereas traders aim to exploit short-term fluctuations. Granger =-=[23]-=- suggested that long memory in economic time series can be due to the aggregation of a cross section of time series with different persistence levels. This argument was proposed by Andersen & Bollersl... |

204 |
Spin glass theory and beyond. World scientific lecture notes in physics 9
- Mézard, Parisi, et al.
- 1987
(Show Context)
Citation Context ...the thresholds. The fact that N(t) itself follows a Markov chain means that the population distribution of thresholds is a random measure on {0, ..., N}, which is characteristic of disordered systems =-=[44]-=-, even if we start from a deterministic set of values for the initial thresholds (even identical ones). Here the disorder is endogenous and is generated by the random updating mechanism. • Excess vola... |

168 | Empirical Properties of Asset Returns: Stylized Facts and Statistical Issues
- Cont
- 2001
(Show Context)
Citation Context ...oduction The study of statistical properties of financial time series has revealed a wealth of interesting stylized facts which seem to be common to a wide variety of markets, instruments and periods =-=[12, 16, 25, 47]-=-: • Excess volatility: many empirical studies point out to the fact that it is difficult to justify the observed level of variability in asset returns by variations in “fundamental” economic variables... |

156 |
Heterogeneous information arrivals and return volatility dynamics; uncovering the longrun in high frequency returns
- Andersen, Bollerslev
- 1997
(Show Context)
Citation Context ...ggested that long memory in economic time series can be due to the aggregation of a cross section of time series with different persistence levels. This argument was proposed by Andersen & Bollerslev =-=[1]-=- as a possible explanation for volatility clustering in terms of aggregation of different information flows. The effects of the diversity in time horizons on price dynamics have also been studied by L... |

151 |
Long term memory in stock market prices
- Lo
- 1991
(Show Context)
Citation Context ...k returns could exhibit long range dependence was first suggested by Mandelbrot [41] and subsequently observed in many empirical studies using R/S analysis [42]. Such tests have been criticized by Lo =-=[37]-=- who pointed out that, after accounting for short range dependence, they might yield a different result and proposed a modified test statistic. Lo’s statistic highly depends on the way “short range” d... |

144 | On the detection and estimation of long memory in stochastic volatility
- Breidt, Crato, et al.
- 1998
(Show Context)
Citation Context ...ponential decay in autocorrelations of absolute or squared returns, the empirical autocorrelations are similar to a power law [13, 25]: C |r|(τ) = corr(|rt|, |rt+τ |) � c τ β with an exponent β ≤ 0.5 =-=[13, 9]-=-, which suggests the presence of “long-range” dependence in amplitudes of returns, discussed below. 2.2 Long range dependence Let us recall briefly the commonly used definitions of long range dependen... |

135 |
Modelling volatility persistence of speculative returns: A new approach
- Ding, Granger
- 1996
(Show Context)
Citation Context ... periods and is regarded as a typical manifestation of volatility clustering [8, 13, 16, 25]. Similar behavior is observed for the autocorrelation of squared returns [8] and more generally for |rt| α =-=[16, 17, 13]-=- but it seems to be most significant for α = 1 i.e. absolute returns [16]. GARCH models [8, 19] were among the first models to take into account the volatility clustering phenomenon. In a GARCH(1,1) m... |

126 |
ARCH Modeling in Finance
- Bollerslev, Chou, et al.
- 1992
(Show Context)
Citation Context ...figure 2 (right) shows this decay for SLM stock (NYSE). This observation is remarkably stable across asset classes and time periods and is regarded as a typical manifestation of volatility clustering =-=[8, 13, 16, 25]-=-. Similar behavior is observed for the autocorrelation of squared returns [8] and more generally for |rt| α [16, 17, 13] but it seems to be most significant for α = 1 i.e. absolute returns [16]. GARCH... |

119 |
The econometrics of financial markets
- Pagan
- 1996
(Show Context)
Citation Context ...oduction The study of statistical properties of financial time series has revealed a wealth of interesting stylized facts which seem to be common to a wide variety of markets, instruments and periods =-=[12, 16, 25, 47]-=-: • Excess volatility: many empirical studies point out to the fact that it is difficult to justify the observed level of variability in asset returns by variations in “fundamental” economic variables... |

116 |
What moves stock prices
- Cutler, Poterba, et al.
- 1989
(Show Context)
Citation Context ...urns by variations in “fundamental” economic variables. In particular, the occurrence of large (negative or positive) returns is not always explainable by the arrival of new information on the market =-=[15]-=-. • Heavy tails: the (unconditional) distribution of returns displays a heavy tail with positive excess kurtosis. ⋆ The author thanks Alan Kirman and Gilles Teyssière for their infinite patience and p... |

102 | Time series properties of an artificial stock market
- LeBaron, Arthur, et al.
- 1999
(Show Context)
Citation Context ...dered modeling financial markets by analogy with ecological systems where various trading strategies co-exist and evolve via a “natural selection” mechanism, according to their relative profitability =-=[2, 3, 34, 32]-=-. The idea of these models, the prototype of which is the Santa Fe artificial stock market [3, 34], is that a financial market can be viewed as a population of agents, identified by their (set of) dec... |

100 |
The socio-economic dynamics of speculative markets: interacting agents, chaos, and fat tails of return distributions
- Lux
- 1998
(Show Context)
Citation Context ...ed models of financial markets. Agent-based market models attempt to explain the origin of the observed behavior of market prices in terms of simple, stylized, behavioral rules of market participants =-=[11, 38, 39, 32]-=-: in this approach a financial market is modeled as a system of heterogeneous, interacting agents and several examples of such models have been shown to generate price behavior similar to those observ... |

89 | Occasional structural breaks and long memory with an application to the S&P500 absolute stock returns
- Granger, Hyung
- 2004
(Show Context)
Citation Context ... The robustness of these empirical facts call for an explanation, which “non-stationarity” does not provide. Of course, these mechanisms are not mutually exclusive: a recent study by Granger and Hyng =-=[24]-=- illustrates the interplay of these two effects by combining an underlying long memory process with occasional structural breaks. Independently of the econometric debate on the “true nature” of the re... |

89 |
Volatility Clustering in Financial Markets: a MicroSimulation of Interacting Agents
- Lux, Marchesi
- 2000
(Show Context)
Citation Context ...ed models of financial markets. Agent-based market models attempt to explain the origin of the observed behavior of market prices in terms of simple, stylized, behavioral rules of market participants =-=[11, 38, 39, 32]-=-: in this approach a financial market is modeled as a system of heterogeneous, interacting agents and several examples of such models have been shown to generate price behavior similar to those observ... |

81 | Agent-based computational finance: suggested readings and early research
- LeBaron
(Show Context)
Citation Context ...n Section 3 and discuss how they lead to volatility clustering. Most of these agent-based models are complex in structure and have been studied using Monte Carlo simulations. As noted also by LeBaron =-=[31]-=-, due to the complexity of such models it is often not clear which aspect of the model is responsible for generating the stylized facts and whether all the ingredients of the model are indeed required... |

68 | Arbitrage with fractional Brownian motion
- Rogers
- 1997
(Show Context)
Citation Context ...n motion: since fractional Brownian motion is not a semimartingale, a model in which the (log)-price are described by a fractional Brownian motion is not arbitrage-free (in the continuous-time sense) =-=[51]-=-. This result (and the fact that fractional Brownian motions fails to be a semimartingale) crucially depends on the local behavior of its sample paths, not on its long range dependence property. Cheri... |

61 |
Using renewal processes to generate long range dependence and high variability
- Taqqu, Levy
- 1986
(Show Context)
Citation Context ...es10 Rama Cont long-range dependence in absolute returns. More important than the switching is the fact the time spent in each regime –the duration of regimes– should have a heavy-tailed distribution =-=[48, 52]-=-. By contrast with Markov switching, which leads to short range correlations, this mechanism has been called “renewal switching”. 2 Bayraktar et al. [6] study a model where an order flow with random, ... |

60 |
Robust R/S analysis of long–run serial correlations
- Mandelbrot, Taqqu
- 1979
(Show Context)
Citation Context ...f many empirical studies. The idea that stock returns could exhibit long range dependence was first suggested by Mandelbrot [41] and subsequently observed in many empirical studies using R/S analysis =-=[42]-=-. Such tests have been criticized by Lo [37] who pointed out that, after accounting for short range dependence, they might yield a different result and proposed a modified test statistic. Lo’s statist... |

51 | Limit theory for the sample autocorrelations and extremes of a GARCH(1,1) process
- Mikosch, Stărică
- 2000
(Show Context)
Citation Context ... where the sample ACF is consistent, its estimation error can have a heavy-tailed asymptotic distribution, leading to large errors. The situation is even worse for autocorrelations of squared returns =-=[45]-=-. Thus, one must be cautious in identifying behavior of sample autocorrelation with the autocorrelations of the return process. Slow decay of sample autocorrelation functions may possibly arise from o... |

46 |
Recruitment,” Quarterly
- Kirman, “Ants
- 1993
(Show Context)
Citation Context ...e instances of such models. 3.3 Behavioral switching The economic literature contains examples where switching of economic agents between two behavioral patterns leads to large aggregate fluctuations =-=[29]-=-: in the context of financial markets, these behavioral patterns can be seen as trading rules and the resulting aggregate fluctuations as large movements in the market price i.e. heavy tails in return... |

45 |
When Can Price be Arbitraged Efficiently? A Limit to the Validity of the Random Walk and Martingale Models
- Mandelbrot
- 1971
(Show Context)
Citation Context ...n example is shown in figure 2 (left). This “spectral whiteness” of returns can be attributed to the activity of arbitrageurs who exploit linear correlations in returns via trend following strategies =-=[41]-=-. By contrast, the autocorrelation function of absolute returns remains positive over lags of several weeks and decays slowly to zero: figure 2 (right) shows this decay for SLM stock (NYSE). This obse... |

32 | Microeconomic models for long memory in the volatility of financial time series
- Kirman, Teyssiére
(Show Context)
Citation Context ...and the resulting aggregate fluctuations as large movements in the market price i.e. heavy tails in returns. Recently, models based on this idea have also been shown to generate volatility clustering =-=[30, 39]-=-. Lux and Marchesi [39] study an agent-based model in which heavy tails of asset returns and volatility clustering arise from behavioral switching of market participants between fundamentalist and cha... |

31 | Bubbles, crashes, and intermittency in agent based market models
- Giardina, Bouchaud
- 2003
(Show Context)
Citation Context ...vytailed durations could lead to volatility clustering. Although in the agentbased models discussed above, it may not be easy to speak of well-defined “regimes” of activity, but Giardina and Bouchaud =-=[21]-=- argue that this is indeed the mechanism which generates volatility clustering in the Lux-Marchesi [39] and other models discussed above. In these models, agents switch between strategies based on the... |

30 |
Modeling Long Memory in Stock Market Volatility
- Liu
- 2000
(Show Context)
Citation Context ...g of opinions. Simulation of this model exihibit autocorrelation patterns in absolute returns with a behavior similar to that described in Section 2. 3.4 The role of investor inertia As argued by Liu =-=[35]-=-, the presence of a Markovian regime switching mechanism in volatility can lead to volatility clustering, is not sufficient to generates10 Rama Cont long-range dependence in absolute returns. More imp... |

28 |
2000) Long memory in stock-market trading volume
- Lobato, Velasco
(Show Context)
Citation Context ... a several weeks. • Volume/volatility correlation: trading volume is positively correlated with market volatility. Moreover, trading volume and volatility show the same type of “long memory” behavior =-=[36]-=-. Among these properties, the phenomenon of volatility clustering has intrigued many researchers and oriented in a major way the development of stochastic models in finance –GARCH models and stochasti... |

22 |
On defining long range dependence
- Heyde, Yang
- 1997
(Show Context)
Citation Context ...mpirical conclusions are therefore less clear [54]. However, the absence of long range dependence in returns may be compatible with its presence in absolute returns or “volatility”. As noted by Heyde =-=[26]-=-, one should distinguish long range dependence in signs of increments, when sign(rt) verifies (3), from long range dependence in amplitudes, when |rt| verifies (3). Asset returns do not seem to posses... |

20 | Statistical properties of genetic learning in a model of exchange rate
- Arifovic, Gencay
- 2000
(Show Context)
Citation Context ...dered modeling financial markets by analogy with ecological systems where various trading strategies co-exist and evolve via a “natural selection” mechanism, according to their relative profitability =-=[2, 3, 34, 32]-=-. The idea of these models, the prototype of which is the Santa Fe artificial stock market [3, 34], is that a financial market can be viewed as a population of agents, identified by their (set of) dec... |

17 |
A critical look at Lo's modified R/S statistic
- Teverovsky, Taqqu, et al.
- 1999
(Show Context)
Citation Context ... a different result and proposed a modified test statistic. Lo’s statistic highly depends on the way “short range” dependence is accounted for and shows a bias towards rejecting long range dependence =-=[53]-=-. The final empirical conclusions are therefore less clear [54]. However, the absence of long range dependence in returns may be compatible with its presence in absolute returns or “volatility”. As no... |

17 |
The Power of Patience: A Behavioral Regularity in Limit Order Placement
- Zovko, Farmer
(Show Context)
Citation Context ... can be seen as a stylized version of various estimators of volatility based on moving averages of absolute or squared returns. It is also corroborated by a recent empirical study by Zovko and Farmer =-=[55]-=-, who show that traders use recent volatility as a signal when placing orders. The asynchronous updating scheme proposed here avoids introducing an artificial ordering of agents as in sequential choic... |

16 | A limit theorem for financial markets with inert investors
- Bayraktar, Horst, et al.
- 2006
(Show Context)
Citation Context ...s– should have a heavy-tailed distribution [48, 52]. By contrast with Markov switching, which leads to short range correlations, this mechanism has been called “renewal switching”. 2 Bayraktar et al. =-=[6]-=- study a model where an order flow with random, heavytailed, durations between trades leads to long range dependence in returns. When the durations τn of the inactivity periods have a distribution of ... |

14 | Bifurcation routes to volatility clustering under evolutionary learning, CeNDEF Working paper 03{03
- Gaunersdorfer, Hommes, et al.
- 2003
(Show Context)
Citation Context ...ion by a deterministic dynamical system which, through the complex price dynamics it generate, are able to mimick some “statistical” properties of the returns process, including volatility clustering =-=[28]-=-. Though the Santa Fe market model is capable of qualitatively replicating some of the stylized facts [34], precise comparisons with empirical observations are still lacking. Indeed, given the large n... |

12 |
From the bird’s eye view to the microscope: a survey of new stylized facts of the intra-daily foreign exchange markets’, Finance and Stochastics
- Guillaume, Dacorogna, et al.
- 1997
(Show Context)
Citation Context |

11 |
Scaling in financial data: stable laws and beyond
- Cont, Bouchaud, et al.
- 1997
(Show Context)
Citation Context ...figure 2 (right) shows this decay for SLM stock (NYSE). This observation is remarkably stable across asset classes and time periods and is regarded as a typical manifestation of volatility clustering =-=[8, 13, 16, 25]-=-. Similar behavior is observed for the autocorrelation of squared returns [8] and more generally for |rt| α [16, 17, 13] but it seems to be most significant for α = 1 i.e. absolute returns [16]. GARCH... |

9 | 2005. “Heterogeneity and Feedback in an Agent-based Market Model - Ghoulmie, Cont, et al. |

7 |
2004), Gaussian moving averages, semimartingales and option pricing. Stochastic Process
- Cheridito
(Show Context)
Citation Context ...ply long-range dependence in any way: αstable Lévy processes provide examples of self-similar processes with independent increments. Nor is self-similarity implied by long range dependence: Cheridito =-=[10]-=- gives several examples of Gaussian semimartingales with the same long range dependence features as fractional Brownian noise but with no self-similarity (thus very different “short range” properties ... |

6 |
Long range dependence and stock returns
- Willinger, Taqqu, et al.
- 1999
(Show Context)
Citation Context ...non. Also, it has inspired much debate as to whether there is long-range dependence in volatility. We review some of these issues in Section 2. As noted by the participants of this econometric debate =-=[54, 46]-=-, statistical analysis alone is not likely to provide a definite answer for the presence or absence of long-range dependence phenomenon in stock returns or volatility, unless economic mechanisms are p... |

4 |
How misleading can sample ACFs of stable MAs be
- Resnick, Samorodnitsky, et al.
- 1999
(Show Context)
Citation Context ... fail to work [50]. For example, sample autocorrelation functions may fail to be consistent estimators of the true autocorrelation of returns in the price generating process: Resnick and van der Berg =-=[49]-=- give examples of such processes where sample autocorrelations converge to random values as sample size grows! Also, in cases where the sample ACF is consistent, its estimation error can have a heavy-... |

4 |
Why Non-linearities Can Ruin the Heavy-tailed Modeller’s Day
- RESNICK
- 1998
(Show Context)
Citation Context ...tc. but if time series of asset returns indeed possess the two features of heavy tails and long range dependence, then many of the standard estimation procedures for these quantities may fail to work =-=[50]-=-. For example, sample autocorrelation functions may fail to be consistent estimators of the true autocorrelation of returns in the price generating process: Resnick and van der Berg [49] give examples... |

3 |
Asset price dynamics among heterogeneous interacting agents
- Chiarella, Gallegati, et al.
(Show Context)
Citation Context ...ed models of financial markets. Agent-based market models attempt to explain the origin of the observed behavior of market prices in terms of simple, stylized, behavioral rules of market participants =-=[11, 38, 39, 32]-=-: in this approach a financial market is modeled as a system of heterogeneous, interacting agents and several examples of such models have been shown to generate price behavior similar to those observ... |

2 |
volatility as a simple generator of apparent financial power laws and long
- Stochastic
(Show Context)
Citation Context ...ets 7 in signs [26]. Many authors have thus suggested models, such as FIGARCH [4], in which returns have no autocorrelation but their amplitudes have long range dependence [4, 18]. It has been argued =-=[33, 5]-=- that the decay of C |r|(τ) can also be reproduced by a superposition of several exponentials, indicating that the dependence is characterized by multiple time scales. In fact, an operational definiti... |

2 |
Mandelbrot (1963) The variation of certain speculative prices
- B
(Show Context)
Citation Context ...ations of asset returns are often insignificant, except for very small intraday time scales (� 20 minutes) where microstructure effects come into play. • Volatility clustering: as noted by Mandelbrot =-=[40]-=-, “large changes tend to be followed by large changes, of either sign, and small changes tend to be followed by small changes.” A quantitative manifestation of this fact is that, while returns themsel... |

1 |
Asset pricing under heterogeneous expectations in an artificial stock market, in: The Economy as an Evolving Complex System. Perseus Books
- Arthur, Holland, et al.
- 1997
(Show Context)
Citation Context ...dered modeling financial markets by analogy with ecological systems where various trading strategies co-exist and evolve via a “natural selection” mechanism, according to their relative profitability =-=[2, 3, 34, 32]-=-. The idea of these models, the prototype of which is the Santa Fe artificial stock market [3, 34], is that a financial market can be viewed as a population of agents, identified by their (set of) dec... |

1 |
Threshold behavior and volatility clustering in financial markets, Working paper, Ecole Polytechnique
- Cont, Ghoulmie, et al.
- 2004
(Show Context)
Citation Context ...k to the level of agent behavior, partly because the models described above contain various other ingredients whose contribution to the overall behavior is thus blurred. We now discuss a simple model =-=[14]-=- reproducing several stylized empirical facts, where the origin of volatility clustering can be clearly traced back to investor inertia, caused by threshold response of investors to news arrivals. 2 S... |

1 |
dependence effects and ARCH modeling, in Theory and applications of long-range dependence, Birkhäuser
- Long-range
- 2003
(Show Context)
Citation Context ...non. Also, it has inspired much debate as to whether there is long-range dependence in volatility. We review some of these issues in Section 2. As noted by the participants of this econometric debate =-=[54, 46]-=-, statistical analysis alone is not likely to provide a definite answer for the presence or absence of long-range dependence phenomenon in stock returns or volatility, unless economic mechanisms are p... |