Modeling Ultra-High-Frequency Data: The S&P 500 Index Future

Marco Minozzo () and Silvia Centanni ()
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Marco Minozzo: University of Perugia
Silvia Centanni: University of Verona

A chapter in Mathematical and Statistical Methods in Insurance and Finance, 2008, pp 165-172 from Springer

Abstract: Abstract In recent years, marked point processes have found a natural application in the modeling of ultra-high-frequency financial data. The use of these processes does not require the integration of the data which is usually needed by other modeling approaches. Two main classes of marked point processes have so far been proposed to model financial data: the class of the autoregressive conditional duration models of Engle and Rüssel and the broad class of doubly stochastic Poisson processes with marks. In this paper, we show how to model an ultra-high-frequency data set relative to the prices of the future on the S&P 500 index using a particular class of doubly stochastic Poisson process. Our models allow a natural interpretation of the underlying intensity in terms of news reaching the market and does not require the use of ad hoc methods to treat the seasonalities. Filtering and estimation are carried out by Monte Carlo expectation maximization and reversible jump Markov chain Monte Carlo algorithms.

Keywords: Cox process; Marked point process; Monte Carlo expectation maximization; Reversible jump Markov chain Monte Carlo; Shot noise process; Tick by tick data (search for similar items in EconPapers)
Date: 2008
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-88-470-0704-8_21

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DOI: 10.1007/978-88-470-0704-8_21

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