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WAITING TIME DISTRIBUTIONS FOR FINANCIAL MARKETS

WAITING TIME DISTRIBUTIONS FOR FINANCIAL MARKETS. Lorenzo Sabatelli 1,2 , Shane Keating 1 , Jonathan Dudley 1 and Peter Richmond 1 1 Department of Physics, Trinity College Dublin 2, Ireland and 2 Hibernian Investment Managers, IFSC, Dublin 1, Ireland.

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WAITING TIME DISTRIBUTIONS FOR FINANCIAL MARKETS

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  1. WAITING TIME DISTRIBUTIONS FOR FINANCIAL MARKETS Lorenzo Sabatelli1,2, Shane Keating1, Jonathan Dudley1 and Peter Richmond11 Department of Physics, Trinity College Dublin 2, Irelandand2 Hibernian Investment Managers, IFSC, Dublin 1, Ireland The authors acknowledge support from the EU via Marie Curie Industrial Fellowship MCFH-1999-00026

  2. Objective • waiting time distribution (WTD) for the Irish stock market 1850 to 1854. • 10 stocks out of a database of 60 are examined. • waiting time distributionsvary from a day to some months are • compare with WTD for Japanese yen currency returns 1989-1998 • waiting times vary from a minute to over an hour

  3. 19th century Irish Stock Exchange • Deals done 'matched bargain basis' • members of exchangebring buyers and sellers together • Essentially same as today • Today, many more buyers and sellers. • Recent studies of 19th century markets find they were well integrated • Dublin traded international shares • Not solely a regional market. • World trends reflected in the Irish market • No exchange controls. • From 1801 to 1922 Ireland was part of UK • Largest shares: Banks and key railways – • Quality investments for UK investors • Also traded in London.

  4. Random walks Time Time

  5. Markovian Random walk Continuous time random walk Montroll & Weiss 1965

  6. Fourier Laplace Transform

  7. Choice for memory function Ф

  8. Results: Irish Stock Market data

  9. Results: Yen Currency Market data

  10. Conclusions: • Irish data, • outside the cut off regime, survival time distribution exhibits two clear regions • can be well fitted by Mittag Leffler function • power law tail has exponent of magnitude less than unity (~ 0.4) • Japanese yen • short waiting times (1 to 30 minutes) fits power law over large range • but exponent greater than unity (~ 1.9) • larger values of time shows a smaller power law regime having an exponent between 0.9 and 1.1 that is • at the border of the regime that can be fitted with a Mittag Leffler function. • for larger waiting times, data exhibit two ‘humps’. • The characteristic time could be associated with opening and closing of the major global trading centres.

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