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## Modelling systemic cojumps with Hawkes factor models (2013)

### Citations

710 | Transform analysis and asset pricing for affine jumpdiffusions
- Duffie, Pan, et al.
- 2000
(Show Context)
Citation Context ... empirical analysis [8, 9, 10, 11, 12, 13], and applications to asset ∗These authors contributed equally to this work. 1www.quantlab.it 1 ar X iv :1 30 1. 61 41 v1s[ qfin .ST ]s25sJa n 2 01 3 pricing =-=[14, 15, 16, 17, 18]-=-. General review on jumps are [19] and [20]. However, there has been less research on cojumps (i.e. simultaneous jumps in two or more stock prices) and most are of empirical nature such as [21, 22, 23... |

612 |
Financial modelling with Jump Processes
- CONT, TANKOV
- 2003
(Show Context)
Citation Context ...plications to asset ∗These authors contributed equally to this work. 1www.quantlab.it 1 ar X iv :1 30 1. 61 41 v1s[ qfin .ST ]s25sJa n 2 01 3 pricing [14, 15, 16, 17, 18]. General review on jumps are =-=[19]-=- and [20]. However, there has been less research on cojumps (i.e. simultaneous jumps in two or more stock prices) and most are of empirical nature such as [21, 22, 23, 24]; exceptions are the papers o... |

332 | Power and Bipower Variation with Stochastic Volatility and Jumps.
- Barndorff-Nielsen, Shephard
- 2004
(Show Context)
Citation Context ...we can follow several strategies available in literature. We base our approach on the realized absolute variation and the realized bipower variation, whose asymptotic theory is treated for example in =-=[47]-=-. Our estimators of local volatility based on these quantities are defined by the exponentially weighted moving averages σ̂abs,t = µ −1 1 α ∑ i>0 (1− α)i−1|rt−i| (1) and σ̂2bv,t = µ −2 1 α ∑ i>0 (1− α... |

273 |
Intraday periodicity and volatility persistence in financial markets.
- Andersen, Bollerslev
- 1997
(Show Context)
Citation Context ...ough the plot of the autocorrelations of absolute intraday returns. A.4 Volatility proxy For estimating the local volatility, we use the realized absolute variation and the realized bipower variation =-=[55, 47]-=-. Let the logarithmic prices p(t) be generated by a process dp(t) = µ(t) dt+ σ(t) dW (t), (10) with µ(t) a finite variation process, σ(t) a càdlàg volatility process, W (t) a standard Brownian motio... |

234 | Do Stock Prices and Volatility Jump? Reconciling Evidence from Spot and Option Prices.
- Eraker
- 2004
(Show Context)
Citation Context ... empirical analysis [8, 9, 10, 11, 12, 13], and applications to asset ∗These authors contributed equally to this work. 1www.quantlab.it 1 ar X iv :1 30 1. 61 41 v1s[ qfin .ST ]s25sJa n 2 01 3 pricing =-=[14, 15, 16, 17, 18]-=-. General review on jumps are [19] and [20]. However, there has been less research on cojumps (i.e. simultaneous jumps in two or more stock prices) and most are of empirical nature such as [21, 22, 23... |

231 |
Statistical models for earthquake occurrences and residual analysis for point processes
- OGATA
- 1988
(Show Context)
Citation Context ...se the use of a class of self-exciting point processes, termed Hawkes processes. These processes were introduced more than forty years ago [32], and have been widely employed to model earthquake data =-=[33, 34, 35]-=-. In the last years, Hawkes processes have experienced an increasing popularity in mathematical finance and econometrics. One of the first applications to financial time series is due to [36], and a w... |

229 |
Econometrics of testing for jumps in financial economics using bipower variation.
- Barndorff-Nielsen, Shephard
- 2006
(Show Context)
Citation Context ...sses and the only dependence is possibly in the size of the jumps. An incomplete list of recent studies on jumps following this approach includes theoretical work on nonparametric jump identification =-=[1, 2, 3, 4, 5, 6, 7]-=-, as well as empirical analysis [8, 9, 10, 11, 12, 13], and applications to asset ∗These authors contributed equally to this work. 1www.quantlab.it 1 ar X iv :1 30 1. 61 41 v1s[ qfin .ST ]s25sJa n 2 0... |

207 |
An Introduction to the Theory of Point Processes. Vol. II. Probability and its Applications
- Daley, Vere-Jones
- 2008
(Show Context)
Citation Context ... provide the main results needed for the remaining of the paper, but for a complete mathematical treatment of Hawkes and more general point processes we refer the reader to the comprehensive textbook =-=[50]-=-. A univariate point process Nt 6 is called a Hawkes process if it is a linear self-exciting process, defined by the intensity I(t) = λ(t) + ∫ t −∞ ν(t− u)dNu = λ(t) + ∑ ti<t ν(t− ti) , (8) where λ is... |

173 |
Spectra of some self-exciting and mutually exciting point processes
- Hawkes
- 1971
(Show Context)
Citation Context ...l the time clustering of jumps for individual assets we propose the use of a class of self-exciting point processes, termed Hawkes processes. These processes were introduced more than forty years ago =-=[32]-=-, and have been widely employed to model earthquake data [33, 34, 35]. In the last years, Hawkes processes have experienced an increasing popularity in mathematical finance and econometrics. One of th... |

89 |
On Lewis’ simulation method for point processes.
- Ogata
- 1981
(Show Context)
Citation Context ...um likelihood estimator of the Hawkes process parameters that we employ in this paper has been developed in [51] and [52], while the simulation algorithm we use is based on the procedure discussed in =-=[53]-=-, which directly derives from the Shedler-Lewis thinning algorithm, [54]. 0 10 20 30 w (minute) 0 0.005 0.01 0.015 p̂ M J w Empirical Monte Carlo mean Monte Carlo 99% c.l. Monte Carlo 95% c.l. 0 250 5... |

78 |
Disentangling Diffusion from Jumps
- AÏT-SAHALIA
- 2004
(Show Context)
Citation Context ...sses and the only dependence is possibly in the size of the jumps. An incomplete list of recent studies on jumps following this approach includes theoretical work on nonparametric jump identification =-=[1, 2, 3, 4, 5, 6, 7]-=-, as well as empirical analysis [8, 9, 10, 11, 12, 13], and applications to asset ∗These authors contributed equally to this work. 1www.quantlab.it 1 ar X iv :1 30 1. 61 41 v1s[ qfin .ST ]s25sJa n 2 0... |

71 | Jumps in Financial Markets: a New Nonparametric Test and Jump Dynamics,” Review of Financial studies,
- Lee, Mykland
- 2008
(Show Context)
Citation Context ...sses and the only dependence is possibly in the size of the jumps. An incomplete list of recent studies on jumps following this approach includes theoretical work on nonparametric jump identification =-=[1, 2, 3, 4, 5, 6, 7]-=-, as well as empirical analysis [8, 9, 10, 11, 12, 13], and applications to asset ∗These authors contributed equally to this work. 1www.quantlab.it 1 ar X iv :1 30 1. 61 41 v1s[ qfin .ST ]s25sJa n 2 0... |

68 | News Arrival, Jump Dynamics, and Volatility Components for Individual Stock Returns,”
- Maheu, McCurdy
- 2004
(Show Context)
Citation Context ...of the jumps. An incomplete list of recent studies on jumps following this approach includes theoretical work on nonparametric jump identification [1, 2, 3, 4, 5, 6, 7], as well as empirical analysis =-=[8, 9, 10, 11, 12, 13]-=-, and applications to asset ∗These authors contributed equally to this work. 1www.quantlab.it 1 ar X iv :1 30 1. 61 41 v1s[ qfin .ST ]s25sJa n 2 01 3 pricing [14, 15, 16, 17, 18]. General review on ju... |

67 | Testing for jumps in a discretely observed process.
- Ait-Sahalia, Jacod
- 2009
(Show Context)
Citation Context |

62 | The Flash Crash: The impact of high frequency trading on an electronic market
- Kirilenko, Kyle, et al.
- 2010
(Show Context)
Citation Context ...his synchronization effect had its most spectacular appearance during the May 6, 2010 Flash Crash. According to the SEC-CFTC, the crash started from a rapid price decline in the E-Mini S&P 500 market =-=[28, 29]-=-. However in a very short time the price drop propagated towards ETF, stock indices and their components, and derivatives. For example, the Dow Jones Industrial Average plunged about nine percent, onl... |

60 |
The impact of jumps in equity index volatility and returns,
- Johannes, Polson
- 2003
(Show Context)
Citation Context ... empirical analysis [8, 9, 10, 11, 12, 13], and applications to asset ∗These authors contributed equally to this work. 1www.quantlab.it 1 ar X iv :1 30 1. 61 41 v1s[ qfin .ST ]s25sJa n 2 01 3 pricing =-=[14, 15, 16, 17, 18]-=-. General review on jumps are [19] and [20]. However, there has been less research on cojumps (i.e. simultaneous jumps in two or more stock prices) and most are of empirical nature such as [21, 22, 23... |

54 | Variation, jumps, market frictions and high frequency data in financial econometrics.
- Barndorff-Nielsen, Shephard
- 2007
(Show Context)
Citation Context ...s to asset ∗These authors contributed equally to this work. 1www.quantlab.it 1 ar X iv :1 30 1. 61 41 v1s[ qfin .ST ]s25sJa n 2 01 3 pricing [14, 15, 16, 17, 18]. General review on jumps are [19] and =-=[20]-=-. However, there has been less research on cojumps (i.e. simultaneous jumps in two or more stock prices) and most are of empirical nature such as [21, 22, 23, 24]; exceptions are the papers of [25, 26... |

54 | 2009), “Modelling financial high frequency data using point processes,” in Handbook of Financial Time Series, edited by
- Bauwens, Hautsch
(Show Context)
Citation Context ... an increasing popularity in mathematical finance and econometrics. One of the first applications to financial time series is due to [36], and a wide literature review in this context is collected in =-=[37]-=-. Among more recent developments not covered by the latter reference we mention [38] where these processes are applied to the order flow in a continuous double auction market, [39] for the modelling o... |

53 |
Stochastic models for earthquake occurrence.
- Vere-Jones
- 1970
(Show Context)
Citation Context ...se the use of a class of self-exciting point processes, termed Hawkes processes. These processes were introduced more than forty years ago [32], and have been widely employed to model earthquake data =-=[33, 34, 35]-=-. In the last years, Hawkes processes have experienced an increasing popularity in mathematical finance and econometrics. One of the first applications to financial time series is due to [36], and a w... |

51 | No-Arbitrage Semi-Martingale Restrictions for Continuous-Time Volatility Models Subject to Leverage Effects, Jumps and I.I.D. Noise: Theory and Testable Distributional Implications,”
- Andersen, Bollerslev, et al.
- 2007
(Show Context)
Citation Context ...of the jumps. An incomplete list of recent studies on jumps following this approach includes theoretical work on nonparametric jump identification [1, 2, 3, 4, 5, 6, 7], as well as empirical analysis =-=[8, 9, 10, 11, 12, 13]-=-, and applications to asset ∗These authors contributed equally to this work. 1www.quantlab.it 1 ar X iv :1 30 1. 61 41 v1s[ qfin .ST ]s25sJa n 2 01 3 pricing [14, 15, 16, 17, 18]. General review on ju... |

51 |
Modeling financial contagion using mutually exciting jump processes.
- Ait-Sahalia, Cacho-Diaz, et al.
- 2011
(Show Context)
Citation Context ...ver, there has been less research on cojumps (i.e. simultaneous jumps in two or more stock prices) and most are of empirical nature such as [21, 22, 23, 24]; exceptions are the papers of [25, 26] and =-=[27]-=- on cojump estimation and modelling. Poisson jump processes have the great advantage of being analytically tractable. However one might argue that the jump component of the price process could be desc... |

50 | Multi-scale jump and volatility analysis for highfrequency financial data
- Fan, Wang
- 2007
(Show Context)
Citation Context ...) dt+ σ(t) dW (t) + κ(t) dJ(t), (4) where the three terms on the right hand side are the drift, diffusion and jump components, and a microstructure noise t ∼ i.i.d. N (0, η2). Following Fan and Wang =-=[49]-=-, for the dynamics of the volatility σ(t) we take the Geometric Ornstein-Uhlenbeck model d log σ2(t) = −(0.6802 + 0.1 log σ2(t)) dt+ 0.25 dW ′(t) , (5) with correlation between the Wiener processes W ... |

48 | A discrete-time model for daily S&P500 returns and realized variations: Jumps and leverage effects
- Bollerslev, Kretschmer, et al.
- 2009
(Show Context)
Citation Context ...of the jumps. An incomplete list of recent studies on jumps following this approach includes theoretical work on nonparametric jump identification [1, 2, 3, 4, 5, 6, 7], as well as empirical analysis =-=[8, 9, 10, 11, 12, 13]-=-, and applications to asset ∗These authors contributed equally to this work. 1www.quantlab.it 1 ar X iv :1 30 1. 61 41 v1s[ qfin .ST ]s25sJa n 2 01 3 pricing [14, 15, 16, 17, 18]. General review on ju... |

44 |
Financial econometric analysis at ultra-high frequency: Data handling concerns
- Brownless, Gallo
- 2006
(Show Context)
Citation Context ...tification can be described as follows. First, anomalous values in tick-by-tick price data are detected and removed. The algorithm for the outliers detection that we use is due to Brownlees and Gallo =-=[43]-=- and it is explained in Section A.1 of the Appendix. We find no outliers at all for 13 stocks and few units for the other 7, for the vast majority concentrated on the very first minute of the day. Rem... |

42 |
Maximum likelihood estimation of Hawkes’ self-exciting point process.
- Ozaki
- 1979
(Show Context)
Citation Context ...l discuss in Section 7 of this paper. The theoretical characterization of the maximum likelihood estimator of the Hawkes process parameters that we employ in this paper has been developed in [51] and =-=[52]-=-, while the simulation algorithm we use is based on the procedure discussed in [53], which directly derives from the Shedler-Lewis thinning algorithm, [54]. 0 10 20 30 w (minute) 0 0.005 0.01 0.015 p̂... |

33 |
Testing for Jumps when Asset Prices Are Observed with Noisea “Swap Variance”
- Jiang, Oomen
- 2008
(Show Context)
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30 |
The asymptotic behaviour of maximum likelihood estimators for stationary point processes
- Ogata
- 1978
(Show Context)
Citation Context ...at we will discuss in Section 7 of this paper. The theoretical characterization of the maximum likelihood estimator of the Hawkes process parameters that we employ in this paper has been developed in =-=[51]-=- and [52], while the simulation algorithm we use is based on the procedure discussed in [53], which directly derives from the Shedler-Lewis thinning algorithm, [54]. 0 10 20 30 w (minute) 0 0.005 0.01... |

27 | Threshold bipower variation and the impact of jumps on volatility forecasting.
- Corsi, Pirino, et al.
- 2010
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Citation Context |

27 | Stock price jumps: News and volume play a minor role. Wilmott Magazine,
- Joulin, Lefevre, et al.
- 2008
(Show Context)
Citation Context ... we estimate 5 the local volatility σ and then test whether the ratio between absolute returns and local volatility is above a given threshold, that is, if |r| σ > θ. In this work we take θ = 4 as in =-=[46]-=- and return series are obtained from historical prices as reported in Section 2. In order to estimate the local volatility, we can follow several strategies available in literature. We base our approa... |

23 | Testing for common arrivals of jumps for discretely observed multidimensional processes. Unpublished working paper
- Jacod, Todorov
- 2007
(Show Context)
Citation Context ...nd [20]. However, there has been less research on cojumps (i.e. simultaneous jumps in two or more stock prices) and most are of empirical nature such as [21, 22, 23, 24]; exceptions are the papers of =-=[25, 26]-=- and [27] on cojump estimation and modelling. Poisson jump processes have the great advantage of being analytically tractable. However one might argue that the jump component of the price process coul... |

19 |
Quantifying reflexivity in financial markets: Toward a prediction of flash crashes. Physical Review E,
- Filimonov, Sornette
- 2012
(Show Context)
Citation Context ...e used to introduce a new stochastic model for the variation of tick-by-tick asset price both in one and two dimension able to reproduce the strong microscopic mean reversion and the Epps effect, and =-=[41]-=-, which introduces a measure of the market activity providing a direct access to the level of its endogeneity and as a potential predictor of market micro instabilities. In this paper we use Hawkes pr... |

16 | Detecting Jumps from L’evy Jump Diffusion Processes.
- Lee, Hannig
- 2010
(Show Context)
Citation Context |

16 | Risk, jumps and diversification.
- Bollerslev, Law, et al.
- 2007
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Citation Context |

16 | Financial black swans driven by ultrafast machine ecology,” 2012. Available at SSRN
- Johnson, Zhao, et al.
(Show Context)
Citation Context ..., and derivatives. For example, the Dow Jones Industrial Average plunged about nine percent, only to recover those losses within minutes. The contagion effect can be extremely rapid in liquid markets =-=[30, 31]-=- and leads to a strongly synchronized discontinuous movement of the price of many assets. This type of systemic events can not be described by a model where prices jump following independent processes... |

16 |
Simulation of nonhomogeneous Poisson processes with log linear rate function
- Lewis, Shedler
- 1976
(Show Context)
Citation Context ...in this paper has been developed in [51] and [52], while the simulation algorithm we use is based on the procedure discussed in [53], which directly derives from the Shedler-Lewis thinning algorithm, =-=[54]-=-. 0 10 20 30 w (minute) 0 0.005 0.01 0.015 p̂ M J w Empirical Monte Carlo mean Monte Carlo 99% c.l. Monte Carlo 95% c.l. 0 250 500 w (minute) 0 0.25 0.5 Figure 6: MJ probability test under Hawkes null... |

15 |
Empirical evidence on jumps in the term structure of the us treasury market.
- Dungey, McKenzie, et al.
- 2009
(Show Context)
Citation Context ...16, 17, 18]. General review on jumps are [19] and [20]. However, there has been less research on cojumps (i.e. simultaneous jumps in two or more stock prices) and most are of empirical nature such as =-=[21, 22, 23, 24]-=-; exceptions are the papers of [25, 26] and [27] on cojump estimation and modelling. Poisson jump processes have the great advantage of being analytically tractable. However one might argue that the j... |

15 | Jumps, cojumps and macro announcements.
- Lahaye, Laurent, et al.
- 2011
(Show Context)
Citation Context ...16, 17, 18]. General review on jumps are [19] and [20]. However, there has been less research on cojumps (i.e. simultaneous jumps in two or more stock prices) and most are of empirical nature such as =-=[21, 22, 23, 24]-=-; exceptions are the papers of [25, 26] and [27] on cojump estimation and modelling. Poisson jump processes have the great advantage of being analytically tractable. However one might argue that the j... |

13 |
Some examples of statistical inference applied to earthquake data.
- Vere-Jones, Ozaki
- 1982
(Show Context)
Citation Context ...se the use of a class of self-exciting point processes, termed Hawkes processes. These processes were introduced more than forty years ago [32], and have been widely employed to model earthquake data =-=[33, 34, 35]-=-. In the last years, Hawkes processes have experienced an increasing popularity in mathematical finance and econometrics. One of the first applications to financial time series is due to [36], and a w... |

11 | Modelling trades-through in a limit order book using Hawkes processes
- Toke, Pomponio
- 2012
(Show Context)
Citation Context ...ext is collected in [37]. Among more recent developments not covered by the latter reference we mention [38] where these processes are applied to the order flow in a continuous double auction market, =-=[39]-=- for the modelling of trades-through orders in a limit order book, [40] where Hawkes processes are used to introduce a new stochastic model for the variation of tick-by-tick asset price both in one an... |

8 |
risk premia,” The
- Bollerslev, Todorov, et al.
- 2011
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Citation Context |

8 |
Modelling security markets in continuous time: Intensity based, multivariate point process models.
- Bowsher
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Citation Context ... [33, 34, 35]. In the last years, Hawkes processes have experienced an increasing popularity in mathematical finance and econometrics. One of the first applications to financial time series is due to =-=[36]-=-, and a wide literature review in this context is collected in [37]. Among more recent developments not covered by the latter reference we mention [38] where these processes are applied to the order f... |

7 |
Jump Tails, Extreme Dependencies, and the Distribution of Stock Returns
- Bollerslev, Todorov, et al.
- 2011
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Citation Context |

7 |
Identifying jumps in financial assets: a comparison between nonparametric jump tests.
- Dumitru, Urga
- 2012
(Show Context)
Citation Context ...observations nor to the choice of volatility estimation, we take as final series of jumps the intersection of the six sets of jumps. This should also minimize spurious jump detection, as suggested in =-=[48]-=-. 3.1 Performance of the jump detection methods on simulated data In the next section we will discuss the results that we have found about identified jumps. Preliminarily, we conduct a simulation stud... |

6 | Cojumping: Evidence from the us treasury bond and futures markets
- Dungey, Hvozdyk
- 2012
(Show Context)
Citation Context ...16, 17, 18]. General review on jumps are [19] and [20]. However, there has been less research on cojumps (i.e. simultaneous jumps in two or more stock prices) and most are of empirical nature such as =-=[21, 22, 23, 24]-=-; exceptions are the papers of [25, 26] and [27] on cojump estimation and modelling. Poisson jump processes have the great advantage of being analytically tractable. However one might argue that the j... |

6 |
Muzy, “Modelling microstructure noise with mutually exciting point processes
- Bacry, Delattre, et al.
- 2013
(Show Context)
Citation Context ... the latter reference we mention [38] where these processes are applied to the order flow in a continuous double auction market, [39] for the modelling of trades-through orders in a limit order book, =-=[40]-=- where Hawkes processes are used to introduce a new stochastic model for the variation of tick-by-tick asset price both in one and two dimension able to reproduce the strong microscopic mean reversion... |

5 |
risk premia and realized jump volatility.” Working paper, Federal Reserve Board
- Wright, Zhou, et al.
- 2007
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Citation Context |

5 | Diffusion covariation and co-jumps in bidimensional asset price processes with stochastic volatility and infinite activity lévy jumps
- Gobbi, Mancini
- 2007
(Show Context)
Citation Context ...nd [20]. However, there has been less research on cojumps (i.e. simultaneous jumps in two or more stock prices) and most are of empirical nature such as [21, 22, 23, 24]; exceptions are the papers of =-=[25, 26]-=- and [27] on cojump estimation and modelling. Poisson jump processes have the great advantage of being analytically tractable. However one might argue that the jump component of the price process coul... |

3 |
Systemic Risk and
- Das, Uppal
- 2004
(Show Context)
Citation Context |

3 |
Toke. “market making” in an order book model and its impact on the spread.
- Muni
- 2011
(Show Context)
Citation Context ... applications to financial time series is due to [36], and a wide literature review in this context is collected in [37]. Among more recent developments not covered by the latter reference we mention =-=[38]-=- where these processes are applied to the order flow in a continuous double auction market, [39] for the modelling of trades-through orders in a limit order book, [40] where Hawkes processes are used ... |

3 | Portfolio choice in markets with contagion,” 2012. Available at Arxiv.org:1210.1598[q-fin.PM
- Aı̈t-Sahalia, Hurd
(Show Context)
Citation Context ...the model is able to reproduce both the longitudinal and the cross sectional properties of the multi-asset jump process. Recent approaches sharing some aspects with the current paper are discussed in =-=[27, 42]-=- and [24]. The former design a model of asset returns able to capture periods of crisis characterized by contagion and consider it to solve the problem of optimal investment-consumption for a log-util... |

2 |
Cojumps in stock prices: Empirical evidence,” 2012. Available at SSRN 2028443
- Gilder, Shackleton, et al.
(Show Context)
Citation Context |

2 |
Crash Analysis Continuing Developments. http://www.nanex.net
- Flash
(Show Context)
Citation Context ..., and derivatives. For example, the Dow Jones Industrial Average plunged about nine percent, only to recover those losses within minutes. The contagion effect can be extremely rapid in liquid markets =-=[30, 31]-=- and leads to a strongly synchronized discontinuous movement of the price of many assets. This type of systemic events can not be described by a model where prices jump following independent processes... |