Jumps in Financial Markets: A New Nonparametric Test and Jump Dynamics

This paper introduces a new nonparametric test to detect jump arrival times and realized jump sizes in asset prices up to the intra-day level. We demonstrate that the likelihood of misclassification of jumps becomes negligible when we use high-frequency returns. Using our test, we examine jump dynamics and their distributions in the U.S. equity markets. The results show that individual stock jumps are associated with prescheduled earnings announcements and other company-specific news events. Additionally, S&P 500 Index jumps are associated with general market news announcements. This suggests different pricing models for individual equity options versus index options. ∗Lee is with the Georgia Institute of Technology, Finance Area. Mykland is with the University of Chicago, Department of Statistics. We thank Federico Bandi, George Constantinides, Pietro Veronesi, Ruey Tsay, Matthew Spiegel (the Executive Editor), and two anonymous referees for helpful suggestions and comments. Financial support for this research from the National Science Foundation (DMS-02-04-639), Oscar Mayer Dissertation Fellowships, and the Financial Mathematics Program at the University of Chicago is gratefully acknowledged. Lee also thanks for their comments the participants of the 2006 North American Econometric Society Summer Meeting, the 2006 Far Eastern Meeting of Econometric Society, the International Workshop on Applied Probability, the 6th All-Georgia Finance Conference. Comments are welcome. Please address any correspondence to: Suzanne S. Lee, phone: 404.822.1552, fax: 404.894.6030, email: [email protected]. Financial markets sometimes generate significant discontinuities, so called “Jumps”, in financial variables. A number of recent 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, Cao, and Chen (1997, 2000), Bates (1996), Liu, Longstaff, and Pan (2003), Naik and Lee (1990), Duffie, Pan, and Singleton (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 available from continuous-time models, in which most of aforementioned applications were studied. Our goal in this paper is first to propose a new jump detection technique to resolve such identification problems. Further, we show that our technique provides a model-free tool for characterizing jump dynamics in individual equity and S&P 500 Index returns, which allows us to investigate different model structures for their option pricing. There are primarily two motivations for this study. First, while researchers recognize the presence of jumps in order to better explain the excess kurtosis and skewness of return distributions and implied volatility smiles, we also note the fact that jumps do not come to markets regularly, but their arrivals tend to depend on market information. For instance, Piazzesi (2003) shows incorporating jumps related to market information improves bond pricing models. Given the difficulty of pinning down jump parameters, even with both time series and cross-sectional data in parametric settings, we question how one can simply search observable information relevant to jumps which appear to have so strong impact on pricing securities. To learn about the stochastic features of irregular jump arrivals and their associated market information, it is critical to first develop a robust test to detect jumps. Once detected, one can examine what type of information is dynamically related to jumps to improve pricing models and better explain market phenomena.