Cross-Stock Comparisons of the Relative Contribution of Jumps to Total Price Variance

We examine tests for jumps based on recent asymptotic results; we interpret the tests as Hausman-type tests. Monte Carlo evidence suggests that the daily ratio z-statistic has appropriate size, good power, and good jump detection capabilities revealed by the confusion matrix comprised of jump classification probabilities. We identify a pitfall in applying the asymptotic approximation over an entire sample. Theoretical and Monte Carlo analysis indicates that microstructure noise biases the tests against detecting jumps, and that a simple lagging strategy corrects the bias. Empirical work documents evidence for jumps that account for 7% of stock market price variance. Copyright 2005, Oxford University Press.

[1]  S. Taylor Financial Returns Modelled by the Product of Two Stochastic Processes , 1961 .

[2]  P. Clark A Subordinated Stochastic Process Model with Finite Variance for Speculative Prices , 1973 .

[3]  F. Black,et al.  The Pricing of Options and Corporate Liabilities , 1973, Journal of Political Economy.

[4]  R. C. Merton,et al.  Option pricing when underlying stock returns are discontinuous , 1976 .

[5]  J. Hausman Specification tests in econometrics , 1978 .

[6]  Keith D. C. Stoodley,et al.  Time Series Analysis: Theory and Practice I , 1982 .

[7]  P. Brockwell,et al.  Non‐Parametric Estimation for Non‐Decreasing Lévy Processes , 1982 .

[8]  Stephen L Taylor,et al.  Modelling Financial Time Series , 1987 .

[9]  M. Nimalendran,et al.  Price reversals : Bid-ask errors or market overreaction? , 1990 .

[10]  M. Nimalendran,et al.  Components of short-horizon individual security returns , 1991 .

[11]  T. Royen,et al.  Expansions for the multivariate chi-square distribution , 1991 .

[12]  Joel Hasbrouck,et al.  Assessing the Quality of a Security Market: A New Approach to Transaction-Cost Measurement , 1993 .

[13]  Theo.,et al.  Estimation and testing in models containing both jumps and conditional heteroskedasticity , 1995 .

[14]  Ananth N. Madhavan,et al.  Why Do Security Prices Change? A Transaction-Level Analysis of Nyse Stocks , 1996 .

[15]  A. Gallant,et al.  Using Daily Range Data to Calibrate Volatility Diffusions and Extract the Forward Integrated Variance , 1999, Review of Economics and Statistics.

[16]  Nicholas G. Polson,et al.  The Impact of Jumps in Volatility and Returns , 2000 .

[17]  Francis X. Diebold,et al.  Modeling and Forecasting Realized Volatility , 2001 .

[18]  Michael W. Brandt,et al.  Range-Based Estimation of Stochastic Volatility Models , 2001 .

[19]  N. Shephard,et al.  Non‐Gaussian Ornstein–Uhlenbeck‐based models and some of their uses in financial economics , 2001 .

[20]  F. Diebold,et al.  The Distribution of Realized Exchange Rate Volatility , 2000 .

[21]  F. Diebold,et al.  The distribution of realized stock return volatility , 2001 .

[22]  Luca Benzoni,et al.  An Empirical Investigation of Continuous-Time Equity Return Models , 2001 .

[23]  Telling from Discrete Data Whether the Underlying Continuous-Time Model is a Diffusion , 2002 .

[24]  J. Maheu,et al.  Conditional Jump Dynamics in Stock Market Returns , 2002 .

[25]  Steven Kou,et al.  A Jump Diffusion Model for Option Pricing , 2001, Manag. Sci..

[26]  N. Shephard,et al.  Econometrics of Testing for Jumps in Financial Economics Using Bipower Variation , 2005 .

[27]  Yacine Ait-Sahalia,et al.  How Often to Sample a Continuous-Time Process in the Presence of Market Microstructure Noise , 2003 .

[28]  Tim Bollerslev,et al.  Some Like it Smooth, and Some Like it Rough: Untangling Continuous and Jump Components in Measuring, Modeling, and Forecasting Asset Return Volatility , 2003 .

[29]  N. Shephard,et al.  Power and bipower variation with stochastic volatility and jumps , 2003 .

[30]  A. Gallant,et al.  Alternative models for stock price dynamics , 2003 .

[31]  Thomas H. McCurdy,et al.  News Arrival, Jump Dynamics and Volatility Components for Individual Stock Returns , 2003 .

[32]  Ole E. Barndorff-Nielsen,et al.  Measuring the impact of jumps in multivariate price processes using bipower covariation , 2004 .

[33]  P. Hansen,et al.  An Unbiased Measure of Realized Variance , 2004 .

[34]  Jean Jacod,et al.  A Central Limit Theorem for Realised Power and Bipower Variations of Continuous Semimartingales , 2004 .

[35]  Walter Distaso,et al.  Estimating and Testing Sochastic Volatility Models using Realized Measures , 2004 .

[36]  Yacine Aït-Sahalia,et al.  Disentangling diffusion from jumps , 2004 .

[37]  Jeffrey R. Russell,et al.  Separating Microstructure Noise from Volatility , 2004 .

[38]  George Tauchen,et al.  Simulation Methods for Levy-Driven Carma Stochastic Volatility Models , 2004 .

[39]  Peter Reinhard Hansen,et al.  Realized Variance and IID Market Microstructure Noise , 2004 .

[40]  P. Mykland,et al.  How Often to Sample a Continuous-Time Process in the Presence of Market Microstructure Noise , 2003 .

[41]  Donald W. K. Andrews,et al.  Identification and Inference for Econometric Models , 2005 .

[42]  N. Shephard,et al.  Variation, Jumps, Market Frictions and High Frequency Data in Financial Econometrics , 2005 .

[43]  P. Hansen,et al.  Realized Variance and Market Microstructure Noise , 2005 .

[44]  R. Schilling Financial Modelling with Jump Processes , 2005 .

[45]  Zhou Zhou,et al.  “A Tale of Two Time Scales: Determining Integrated Volatility with Noisy High-Frequency Data” , 2005 .

[46]  N. Shephard,et al.  LIMIT THEOREMS FOR BIPOWER VARIATION IN FINANCIAL ECONOMETRICS , 2005, Econometric Theory.

[47]  T. Bollerslev,et al.  A Semiparametric Framework for Modelling and Forecasting Jumps and Volatility in Speculative Prices , 2006 .

[48]  Giuseppe Cavaliere Stochastic Volatility: Selected Readings , 2006 .

[49]  P. Manimaran,et al.  Modelling Financial Time Series , 2006 .

[50]  T. Bollerslev,et al.  A Discrete-Time Model for Daily S&P500 Returns and Realized Variations: Jumps and Leverage Effects , 2007 .

[51]  R. Oomen,et al.  Testing for Jumps When Asset Prices are Observed with Noise - A Swap Variance Approach , 2007 .

[52]  F. Diebold,et al.  Roughing It Up: Including Jump Components in the Measurement, Modeling, and Forecasting of Return Volatility , 2005, The Review of Economics and Statistics.

[53]  Torben G. Andersen,et al.  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 , 2007 .