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Celebrating StatisticsPapers in honour of Sir David Cox on his 80th birthday$
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A. C. Davison, Yadolah Dodge, and N. Wermuth

Print publication date: 2005

Print ISBN-13: 9780198566540

Published to Oxford Scholarship Online: September 2007

DOI: 10.1093/acprof:oso/9780198566540.001.0001

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PRINTED FROM OXFORD SCHOLARSHIP ONLINE (oxford.universitypressscholarship.com). (c) Copyright Oxford University Press, 2021. All Rights Reserved. An individual user may print out a PDF of a single chapter of a monograph in OSO for personal use. date: 14 May 2021

Are there discontinuities in financial prices?

Are there discontinuities in financial prices?

(p.213) 11 Are there discontinuities in financial prices?
Celebrating Statistics

Neil Shephard (Contributor Webpage)

Oxford University Press

This chapter explores whether there are discontinuities in financial price processes using daily data on the Japanese yen and United States dollar. It opens with a brief description of the data, notation, and models to be used, and then turns to a semi-parametric analysis based on the realized quadratic variation process, which suggests appreciable evidence of discontinuities in the data. The parametric modeling of the local martingale of prices using a Brownian motion plus a compound Poisson process is described. A particle filter is used to fit this model, which is compared with the previous approach. The parametric approach seems to miss almost all the real discontinuities in the process. The chapter ends with a brief discussion of some open problems.

Keywords:   financial econometrics, martingale, particle filter, quadratic variation process, semi-parametric model, volatility, yen-dollar exchange rate

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