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

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@TECHREPORT{Cont04volatilityclustering,

author = {Rama Cont},

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

institution = {},

year = {2004}

}

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### 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

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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... |

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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... |

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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... |

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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... |

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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, ... |

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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... |

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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... |

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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... |

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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... |

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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... |

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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... |

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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... |

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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... |

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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... |

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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... |

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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 ... |

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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... |

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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... |

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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... |

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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... |

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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-... |

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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... |

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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... |

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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... |

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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... |

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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... |