WAITING TIME DISTRIBUTIONS FOR FINANCIAL MARKETS

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WAITING TIME DISTRIBUTIONS FOR FINANCIAL MARKETS

• Lorenzo Sabatelli1,2, Shane Keating1, Jonathan
  Dudley1
• and
• Peter Richmond1 1 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
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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 distributions vary 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

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19th century Irish Stock Exchange

• Deals done 'matched bargain basis'
• members of exchange bring 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.

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Random walks
Time
Time
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Markovian Random walk

• Continuous time random walk Montroll Weiss 1965

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Fourier Laplace Transform
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Choice for memory function ?
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Results Irish Stock Market data
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Results Yen Currency Market data
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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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