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## Jumps in financial markets: A new nonparametric test and jump clustering (2007)

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Citations: | 71 - 4 self |

### Citations

1979 | A theory of the term structure of interest rates.
- Cox, Ingersoll, et al.
- 1985
(Show Context)
Citation Context ...consider a one-factor Affine model and compare with the constant volatility case, studied in Subsection 3.1. The model is as in Heston (1993), which is specified as the square root processes (used by =-=Cox, Ingersoll, and Ross, 1985-=-) dσ 2 (t) = ( θ0 + θ1σ 2 (t) ) dt + ωσ(t)dB(t), (20) where B(t) denotes a Brownian motion. For the simulation, we used the parameter estimates from equity markets found in the empirical study by Baks... |

1512 | A closed-form solution for options with stochastic volatility with applications to bonds and currency options. - Heston - 1993 |

1452 |
Numerical Solution of Stochastic Differential Equations,
- Kloeden, Platen
- 1992
(Show Context)
Citation Context ...s that as we increase the frequency of observation the precision of our test increases. For series generation, we used the Euler-Maruyama stochastic differential equation (SDE) discretization scheme (=-=Kloeden and Platen, 1992-=-), an explicit order 0.5 strong and order 1.0 weak scheme. We discard the burn-in period—the first part of the whole series—to avoid the starting value effect. Throughout, we use the notation �t = 1 2... |

1001 | Option pricing when underlying stock returns are discontinuous,
- Merton
- 1976
(Show Context)
Citation Context ...nt empirical and theoretical studies proved the existence of jumps and their substantial impact on financial management, from portfolio and risk management to option and bond pricing and hedging (see =-=Merton, 1976-=-; Bakshi et al., 1997, 2000; Bates, 1996; Liu et al., 2003; Naik and Lee, 1990; Duffie et al., 2000, and Johannes, 2004). Despite advances in asset pricing models and their inference techniques, the s... |

953 |
Stochastic Processes.
- Ross
- 1996
(Show Context)
Citation Context ...ocess. The number of jumps was set to be one per day. If there is a given number of jumps for some given time (one day in this study), then the Poisson jump arrival time is uniformly distributed (see =-=Ross, 1995-=-). Hence, we randomly select the arrival times from a uniform distribution. σ is set at 30%, as in the previous simulation. The standard deviation of jump size distribution is 16Jumps in Financial Ma... |

710 | Transform analysis and asset pricing for affine jump diffusions,
- Duffie, Pan, et al.
- 2000
(Show Context)
Citation Context ...act on financial management, from portfolio and risk management to option and bond pricing and hedging (see Merton, 1976; Bakshi et al., 1997, 2000; Bates, 1996; Liu et al., 2003; Naik and Lee, 1990; =-=Duffie et al., 2000-=-, and Johannes, 2004). Despite advances in asset pricing models and their inference techniques, the studies have found that jumps are empirically difficult to identify, because only discrete data are ... |

705 | Empirical Performance of Alternative Option Pricing Models.
- Bakshi, Cao, et al.
- 1997
(Show Context)
Citation Context ...nd theoretical studies proved the existence of jumps and their substantial impact on financial management, from portfolio and risk management to option and bond pricing and hedging (see Merton, 1976; =-=Bakshi et al., 1997-=-, 2000; Bates, 1996; Liu et al., 2003; Naik and Lee, 1990; Duffie et al., 2000, and Johannes, 2004). Despite advances in asset pricing models and their inference techniques, the studies have found tha... |

667 | Dynamical Asset Pricing Theory, - Duffie - 1992 |

549 | Jumps and stochastic volatility: Exchange rate processes implicit Deutsche mark options,
- Bates
- 1996
(Show Context)
Citation Context ...ed the existence of jumps and their substantial impact on financial management, from portfolio and risk management to option and bond pricing and hedging (see Merton, 1976; Bakshi et al., 1997, 2000; =-=Bates, 1996-=-; Liu et al., 2003; Naik and Lee, 1990; Duffie et al., 2000, and Johannes, 2004). Despite advances in asset pricing models and their inference techniques, the studies have found that jumps are empiric... |

465 | The Asymptotic Theory of Extreme Order Statistics, - Galambos - 1978 |

437 | Continuous-Time Finance. - Merton - 1990 |

419 | The Jump-Risk Premia Implicit in Options: Evidence from an Integrated Time-Series Study. - Pan - 2002 |

332 | Power and Bipower Variation with Stochastic Volatility and Jumps.
- Barndorff-Nielsen, Shephard
- 2004
(Show Context)
Citation Context ...g S(ti) − log S(ti−1)|| log S(ti−1) − log S(ti−2)|, (6) i=3 has been suggested and shown to be a consistent estimator for the integrated volatility, even when there are jumps in return processes (see =-=Barndorff-Nielsen and Shephard, 2004-=-; and Aït-Sahalia, 2004). Despite the intuition that jumps in a process may impact its volatility estimation, it remains consistent no matter how large or small jumps are mixed with the diffusive part... |

310 | Testing Continuous-Time Models of the Spot Interest Rate.
- Ait-Sahalia
- 1996
(Show Context)
Citation Context ...ity. For another robustness check, we also study the case where the stochastic volatility is driven by a general model that accommodates stochastic elasticity of variance and a nonlinear drift (e.g., =-=Aït-Sahalia, 1996-=-; Aït-Sahalia, 2004; and Bakshi et al., 2005) as dσ 2 (t) = ( θ0 + θ1σ 2 (t) + θ2σ 4 (t) + θ3σ −2) dt + √ ω0 + ω1σ 2 (t) + ω2σ 2ω3dB(t). (21) Again, using the estimates for all the nested models in Ba... |

297 | Stochastic Integration and Differential Equations: A New Approach, - Protter - 1992 |

275 | Micro Effects of Macro Announcements: Real-Time Price Discovery in Foreign Exchange,
- Andersen, Bollerslev, et al.
- 2003
(Show Context)
Citation Context ...FOMC meetings and macroeconomic reports. This empirical finding is consistent with the notion that significant financial market jumps are related to responses to macroeconomic news announcements (see =-=Andersen et al., 2003-=-). 19The Review of Financial Studies / v 00 n 000 2007 Table 5 Dynamics of jump arrival in individual equities and the S&P 500 index Wal Mart (WMT) IBM (IBM) Date Time Size (%) News S Date Time Size ... |

245 | The impact of jumps in volatility and returns. - Eraker, Johannes, et al. - 2003 |

240 | An empirical investigation of continuoustime equity return models. - Andersen, Benzoni, et al. - 2002 |

229 | Econometrics of testing for jumps in financial economics using bipower variation. - Barndorff-Nielsen, Shephard - 2006 |

209 | Probability Approximations via the Poisson Clumping Heuristic. - Aldous - 1989 |

189 | Time-Changed Levy Processes and Option Pricing,” - Carr, Wu - 2004 |

170 |
Alternative models for stock price dynamics.
- Chernov, Gallant, et al.
- 2003
(Show Context)
Citation Context ...ized Method of Moments (GMM), (Simulated) Maximum Likelihood Estimation (MLE), Efficient Method of Moment (EMM), or Bayesian approach (see Bakshi et al., 1997; Bates, 2000; Pan 2002; Schaumburg 2001; =-=Chernov et al., 2003-=-; Eraker, Johannes, and Polson, 2003; Aït-Sahalia, 2004; Piazzesi, 2003; and Aït-Sahalia and Jacod, 2005). As is well known, parametric approaches run the risk of incorrect specification for functiona... |

137 | Bond Yields and the Federal Reserve”, - Piazzesi - 2005 |

119 | A user’s guide to measure theoretic probability. - Pollard - 2001 |

113 |
General equilibrium pricing of options on the market portfolio with discontinuous returns,
- Naik, Lee
- 1990
(Show Context)
Citation Context ...heir substantial impact on financial management, from portfolio and risk management to option and bond pricing and hedging (see Merton, 1976; Bakshi et al., 1997, 2000; Bates, 1996; Liu et al., 2003; =-=Naik and Lee, 1990-=-; Duffie et al., 2000, and Johannes, 2004). Despite advances in asset pricing models and their inference techniques, the studies have found that jumps are empirically difficult to identify, because on... |

111 | Dynamic asset allocation with event risk, - Longstaff, Pan - 2003 |

78 | Disentangling Diffusion from Jumps - AÏT-SAHALIA - 2004 |

55 | 2005), “A Tale of Two Time Scales: Determining Integrated Volatility with Noisy High-Frequency Data - Zhang, Aït-Sahalia, et al. |

54 | Pricing and Hedging Long-Term Options. - Bakshi, Cao, et al. - 2000 |

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 |

50 | Multi-scale jump and volatility analysis for highfrequency financial data - Fan, Wang - 2007 |

46 | Asymptotic expansions for sums of weakly dependent random vectors. - Gotze, Hipp - 1983 |

33 | Anova for diffusions and Ito processes. - Mykland, Zhang - 2006 |

30 | Fisher’s information for discretely sampled Lévy processes. - Ait-Sahalia, Jacod - 2008 |

23 |
Estimation of continuous-time models with an application to equity volatility.
- Bakshi, Ju, et al.
- 2006
(Show Context)
Citation Context ... study the case where the stochastic volatility is driven by a general model that accommodates stochastic elasticity of variance and a nonlinear drift (e.g., Aït-Sahalia, 1996; Aït-Sahalia, 2004; and =-=Bakshi et al., 2005-=-) as dσ 2 (t) = ( θ0 + θ1σ 2 (t) + θ2σ 4 (t) + θ3σ −2) dt + √ ω0 + ω1σ 2 (t) + ω2σ 2ω3dB(t). (21) Again, using the estimates for all the nested models in Bakshi et al., (2005), we obtain results simil... |

22 | Asymptotic expansions for martingales. - Mykland - 1993 |

18 | The Statistical and Economic Role of Jumps in Interest Rates - Johannes - 2004 |

17 | Identifying realized jumps on financial markets. Forthcoming in - Tauchen, Zhou - 2005 |

16 | Dampened power law: Reconciling the tail behavior of financial security returns. - Wu - 2006 |

15 | Event risk, contingent claims and the temporal resolution of uncertainty, Carnegie Mellon University working paper - Collin-Dufresne, Hugonnier - 2001 |

14 | Maximum likelihood estimation of jump processes with applications to finance - Schaumburg - 2001 |

11 | Hedging Derivative Securities and Incomplete Markets: An Epsilon-Arbitrage Approach
- Bertsimas, Kogan, et al.
- 2001
(Show Context)
Citation Context ...jumps makes incomplete markets. The degree of market incompleteness depends on the size and intensity of jumps, which determines the magnitude of derivative hedging error (see Naik and Lee, 1990; and =-=Bertsimas et al., 2001-=-). As a by-product, our test yields both the direction and size of detected jumps, allowing the characterization of jump size distribution as well as stochastic jump intensity. These outcomes allow us... |

11 | A new test for jumps in asset prices, Working paper - Jiang, Oomen - 2005 |

7 |
The impact of jumps in volatility and returns, Journal of Finance (forthcoming
- Eraker, Johannes, et al.
- 2002
(Show Context)
Citation Context ... (GMM), (Simulated) Maximum Likelihood Estimation (MLE), Efficient Method of Moment (EMM), or Bayesian approach (see Bakshi et al., 1997; Bates, 2000; Pan 2002; Schaumburg 2001; Chernov et al., 2003; =-=Eraker, Johannes, and Polson, 2003-=-; Aït-Sahalia, 2004; Piazzesi, 2003; and Aït-Sahalia and Jacod, 2005). As is well known, parametric approaches run the risk of incorrect specification for functionals in their chosen models. This is n... |

3 | Asymptotic expansions for martingales, Annals of Probability - Mykland - 1993 |

2 |
Earnings announcements and option prices. Working Paper
- Dubinsky, M
- 2006
(Show Context)
Citation Context ...es allow jump arrival rates to depend on variables such as latent volatility, latent jump size, or market information in an Affine or non-Affine fashion (see Chernov et al., 2003; Piazzesi, 2003; and =-=Dubinsky and Johannes, 2006-=-, for instance). Though incorporating state variables is intuitively attractive, these existing (computationally intensive) parametric procedures become quite complicated to implement due to the disco... |

2 | A Unpublished Manuscript, Chapter 10. Markov Chain Monte Carlo Methods with Applications,” Graduate - Tsay - 2001 |

1 | ANOVA for Diffusions,” Forthcoming Annals of Statistics - Mykland, Zhang - 2006 |

1 | 27 Review of Financial Studies / v 00 n 000 2007 - Carr, Wu - 2004 |

1 |
Edgeworth Expansions for Realized Volatility and Related Estimators. Working Paper
- 2005a
(Show Context)
Citation Context ...we show that stochastic jump estimates based on our test are accurate. Third, we compare our test to the existing nonparametric jump tests by Barndorff-Nielsen and Shephard (2006) and Jiang and Oomen =-=(2005)-=-. Ours outperforms these others in terms of size and power. Monte Carlo simulation confirms the results as well. After we discuss generally how our test can be applied in asset pricing models, we cond... |