TAILIEUCHUNG - Analysis of High-Frequency Financial Data with S-Plus

This property is required because the empirically observed densities of returns contrast with the Gaussian model [see Pagan 1996]. This rejection results from two stylised facts. First, large price changes appear more frequently than the normal density would lead to expect. Second, there are indications of significant asymmetry in stock returns. In other words, negative and positive price changes do not have the same probability. These two stylised facts are also apparent in implied volatilities. The plot of the volatilities and their corresponding strike prices shows a U-shaped or inverted J- shaped relation. In the literature, this empirical observation has been termed the smile. | Analysis of High-Frequency Financial Data with S-Plus Bingcheng Yan and Eric Zivot Department of Economics University of Washington Copyright 2003 by Bingcheng Yan and Eric Zivot. All Rights Reserved April 4 2003 Revised November 10 2003 1 Introduction High-frequency financial data are observations on financial variables taken daily or at a finer time scale and are often irregularly spaced over time. Advances in computer technology and data recording and storage have made these data sets increasingly accessible to researchers and have driven the data frequency to the ultimate limit for some financial markets time stamped transaction-by-transaction or tick-by-tick data referred to as ultra-high-frequency data by Engle 2000 . For equity markets the Trades and Quotes TAQ database of the New York Stock Exchange NYSE contains all recorded trades and quotes on NYSE AMEX NASDAQ and the regional exchanges from 1992 to present. The Berkeley Options Data Base recorded similar data for options markets from 1976 to 1996. In foreign exchange markets Olsen Associates in Switzerland maintains a data base of indicative FX spot quotes for many major currency pairs published over the Reuters network since the mid 1980 s. These high-frequency financial data sets have been widely used to study various market microstructure related issues including price discovery competition among related markets strategic behavior of market participants and modeling of realtime market dynamics. Moreover high-frequency data are also useful for studying the statistical properties volatility in particular of asset returns at lower frequencies. Excellent surveys on the use of high-frequency financial data sets in financial econometrics are provided by Andersen 2000 Campbell Lo and MacKinlay 1997 Dacarogna et. al. 2001 Ghysels 2000 Goodhart and O Hara 1997 Gourieroux and Jasiak 2001 Lyons 2001 Tsay 2001 and Wood 2000 . Contact information yanbc@ and ezivot@. Data and S-PLUS

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