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Large events on the stock market A study of
high resolution data Kertész János Institute of
Physics, BME
with Adam Zawadowski (BME) Tóth Bence
(BME) György Andor (BME) Doyne Farmer (Santa Fe,
Rome)
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LARGE PRICE CHANGES ON SMALL SCALES
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GM
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LARGE CHANGES, SCALES, CAUSES

• Prices fluctuate large events happen unusually
  often
• In a Gaussian world the Black Tuesday 1929, Black
  Monday 1987, etc. should practically never
  happen
• Similarly (or even more so) Large events on
  small scales
• are significantly frequent (fat tails in price
  distributions).
• Correlations (esp. in the volatility) are
  present.
• Large price changes (LPC-s) are of major
  interest
• Prediction (???) Free lunch (but Efficient
  Market Hypothesis (EMH))
• Understanding mechanism ? Stabilizing markets

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Why large price moves? Price changes due to
news response to external
force Internal market mechanism affects
fluctuation Often no basic reason.
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OTHER STUDIES ON LARGE PRICE CHANGES

• Average shape around LPC-s
• Mostly daily price changes of ? 10, ? 20 days
• Abnormal returns calculated using ? analysis
  (takes into account the general trend by relating
  price to an index). AMEX, NYSE, TSE,
  Johannesburg studied by dif. groups
• Overshooting found
• Up-down asymmetry Either no or weaker
  overreaction for
• increases
• Cox et al. and Atkins et al. compared the
  overreaction to the
• bid-ask spread and concluded that no profit
  could be gained
• Overshooting does not necessarily contradict EMH.

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• Omori law for market crashes (Lillo Mantegna,
  2002)
• There are aftershocks in the volatility described
  by a power law.
• Three events (1987, 1997, 1998), daily data, no
  universal behavior, no signature of
  internal/external origin.
• Exogenous vs. endogenous LPC-s (Sornette and
  Helmstetter, 2003)
• Three events (1987, 1991, 2001). Black Monday
  endo,
• Gorbachev, 9.11 exo
• Power law decay of excess volatility with larger
  exponent
• for exo.

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Smaller but significant in the first 10 mins
Intraday price changes gt (4 ? 8?)
Significant overreaction in the first 20 min-s.
After drop 1.2 in 50 trading minutes at 99
significance level 2.1 400
99! (Too long!)
Buy at event, sell after 400 mins and gain 1.3
with 95 conf where the B/AS was taken into
account.
Be careful, no transaction costs were considered!
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NYSE
NASDAQ
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Relaxation function (characteristic for response)
Response decays significantly faster
Autocorrelation function (characteristic for
steady state)
than autocorrelations
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Stock Markets Double auction, where buyers and
sellers put public limit orders in arbitrary
sequence into the Limit Order Book (LOB). Orders
immediately executed are the market orders. The
rules of execution are regulated in detail. These
are the microscopic laws of the market, and the
LOB contains the microscopic dynamics.
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32 days GSK January 2002
Data from the London Stock Exchange 05.2000 to
12.2002
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variable exponent volatility 0.38 bid-ask
spread 0.38 limit orders placed - bid
0.37 limit orders placed - ask
0.40 cancelations - bid 0.30 cancelations -
ask 0.42
Is slow decay due to psychology or intrinsic to
the market? Simple zero intelligence model leads
to power law decay in excess volatility and
spread with larger exponent (1/2).
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SUMMARY

• Large event in high resolution financial data
• Often overreaction in intraday data.
• The decay of the volatility autocorrelation
  function is slower than that of the response
• Empirics Power law decay of relaxation
  functions of volatility and bid/ask spread,
  imbalance, number of cancellations etc.
  Mysterious 0.4 exponent
• Differenciating between human and intrinsic
• The NASDAQ puzzle (B/A spread)
• Large events are mostly due to liquidity problems
  and not caused by volume (not discussed here but
  our data reinforce this view)